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SMU MB0045 SET 1 SOLUTION


Q1. Show the relationship between required rate of return and coupon rate on the value of a bond.

A1. It is important for prospective bond buyers to know how to determine the price of a bond because it will indicate the yield received should the bond be purchased. In this section, we will run through some bond price calculations for various types of bond instruments. Bonds can be priced at a premium, discount, or at par.

If the bond’s price is higher than its par value, it will sell at a premium because its interest rate is higher than current prevailing rates. If the bond’s price is lower than its par value, the bond will sell at a discount because its interest rate is lower than current prevailing interest rates. When you calculate the price of a bond, you are calculating the maximum price you would want to pay for the bond, given the bond’s coupon rate in comparison to the average rate most investors are currently receiving in the bond market.Required yield or required rate of return is the interest rate that a security needs to offer in orderto encourage investors to purchase it. Usually the required yield on a bond is equal to or greater than the current prevailing interest rates. Fundamentally, however, the price of a bond is the sum of the present values of all expected coupon payments plus the present value of the par value at maturity. Calculating bond price is simple: all we are doing is discounting the known future cash flows. Remember that to calculate present value (PV)
 – 
which is based on the assumption that each payment is re-investedat some interest rate once it is received
 – 
we have to know the interest rate that would earn us aknown future value. For bond pricing, this interest rate is the required yield. (If the concepts of present and future value are new to you or you are unfamiliar with the calculations, refer to
Understanding the Time Value of Money.
Here is the formula for calculating a bond’s price, which uses the basic present value (
PV
formula:
C=couponpayment
n=numberofpayments
i=interestrate,orrequiredyield
M = value at maturity, or par value

The succession of coupon payments to be received in the future is referred to as an ordinary annuity, which is a series of fixed payments at set intervals over a fixed period of time. (Coupons on a straight bond are paid at ordinary annuity.) The first payment of an ordinary annuity occursone interval from the time at which the debt security is acquired. The calculation assumes thistime is the present.You may have guessed that the bond pricing formula shown above may be tedious to calculate,as it requires adding the present value of each future coupon payment. Because these paymentsare paid at an ordinary annuity, however, we can use the shorter PV-of-ordinary-annuity formulathat is mathematically equivalent to the summation of all the PVs of future cash flows. This PV-of-ordinary-annuity formula replaces the need to add all the present values of the future coupon.The following diagram illustrates how present value is calculated for an ordinary annuity:Each full moneybag on the top right represents the fixed coupon payments (future value)received in periods one, two and three. Notice how the present value decreases for those couponpayments that are further into the future the present value of the second coupon payment is worthless than the first coupon and the third coupon is worth the lowest amount today. The farther intothe future a payment is to be received, the less it is worth today is the fundamental concept for which the PV-of-ordinary-annuity formula accounts. It calculates the sum of the present valuesof all future cash flows, but unlike the bond  pricing formula we saw earlier, it doesn’t require that we add the value of each coupon payment. (For more on calculating the time valueof annuities, see Anything but Ordinary: Calculating the Present and Future Value of Annuities  and  Understanding the Time Value of Money.)By incorporating the annuity model into the bond pricing formula, which requires us to alsoinclude the present value of the par value received at maturity, we arrive at the followingformula:
Let’s go through a basic example to find the price of a plain vanilla bond.
 Example 1:
Calculate the price of a bond with a par value of $1,000 to be paid in ten years, a
coupon rate of 10%, and a required yield of 12%. In our example we’ll assume that coupon
payments are made semi-annually to bond holders and that the next coupon payment is expectedin six months. Here are the steps we have to take to calculate the price:
1. Determine the Number of Coupon Payments:
Because two coupon payments will be madeeach year for ten years, we will have a total of 20 coupon payments.
2. Determine the Value of Each Coupon Payment:
Because the coupon payments are semi-
annual, divide the coupon rate in half. The coupon rate is the percentage off the bond’s par value.
As a result, each semi-annual coupon payment will be $50 ($1,000 X 0.05).
3. Determine the Semi-Annual Yield:
Like the coupon rate, the required yield of 12% must bedivided by two because the number of periods used in the calculation has doubled. If we left the

required yield at 12%, our bond price would be very low and inaccurate. Therefore, the requiredsemi-annual yield is 6% (0.12/2).
4. Plug the Amounts Into the Formula:
From the above calculation, we have determined that the bond is selling at a discount; the bondprice is less than its par value because the required yield of the bond is greater than the couponrate. The bond must sell at a discount to attract investors, who could find higher interestelsewhere in the prevailing rates. In other words, because investors can make a larger return inthe market, they need an extra incentive to invest in the bonds.
Accounting for Different Payment Frequencies
 In the example above coupons were paid semi-annually, so we divided the interest rate andcoupon payments in half to represent the two payments per year. You may be now wonderingwhether there is a formula that does not require steps two and three outlined above, which arerequired if the coupon payments occur more than once a year. A simple modification of theabove formula will allow you to adjust interest rates and coupon payments to calculate a bondprice for any payment frequency:Notice that the only modification to the original formula is the addition of 
―F‖, which represents
the frequency of coupon payments, or the number of times a year the coupon is paid. Therefore,for bonds paying annual coupons, F would have a value of one. Should a bond pay quarterlypayments, F would equal four, and if the bond paid semi-annual coupons, F would be two.

Q2. What do you understand by operating cycle?
A2. An operating cycle is the length of time between the acquisition of inventoryand the saleof that inventory and subsequent generation of a profit. The shorter the operating cycle, the fastera business gets areturn on investment(ROI) for the inventory it stocks. As a general rule,companies want to keep their operating cycles short for a number of reasons, but in certainindustries, a long operating cycle is actually the norm. Operating cycles are not tied toaccounting periods, but are rather calculated in terms of how long goods sit in inventory beforesale.When a business buys inventory, it ties up money in the inventory until it can be sold. Thismoney may be borrowed or paid up front, but in either case, once the business has purchasedinventory, those funds are not available for other uses. The business views this as an acceptabletradeoff because the inventory is an investment that will hopefully generate returns, but keeping the operating cycle short is still a goal for most businesses so they can keep their liquidity high.Keeping inventory during a long operating cycle does not just tie up funds. Inventory must bestored and this can become costly, especially with items that require special handling, such as humidity controls or security. Furthermore, inventory can depreciate if it is kept in a store toolong. In the case of perishable goods, it can even be rendered unsalable. Inventory must also beinsured and managed by staff members who need to be paid, and this adds to overall operating expenses. There are cases where a long operating cycle in unavoidable. Wineries and distilleries, forexample, keep inventory on hand for years before it is sold, because of the nature of the business.In these industries, the return on investment happens in the long term, rather than the short term.Such companies are usually structured in a way that allows them to borrow against existinginventory or land if funds are needed tofinanceshort-term operations.Operating cycles can fluctuate. During periods of economic stagnation, inventory tends to sitaround longer, while periods of growth may be marked by more rapid turnover. Certain productscan be consistent sellers that move in and out of inventory quickly. Others, like big ticket items,may be purchased less frequently. All of these issues must be accounted for when makingdecisions about ordering and pricing items for inventory.

Q3. What is the implication of operating leverage for a firm?
A3. Operating leverage is the extent to which a firm uses fixed costs inproducing its goods or offering its services. Fixed costs includeadvertisingexpenses,administrative costs, equipment and technology, depreciation, and taxes, but not interest on debt,which is part of financial leverage. By using fixed production costs, a company can increase itsprofits. If a company has a large percentage of fixed costs, it has a high degree of operatingleverage. Automated and high-tech companies, utility companies, and airlines generally havehigh degrees of operating leverage.As an illustration of operating leverage, assume two firms, A and B, produce and sell widgets.Firm A uses a highly automated production process with robotic machines, whereas firm B
assembles the widgets using primarily semiskilled labour. Table 1 shows both firm’s operating
cost structures.Highly automated firm A has fixed costs of $35,000 per year and variable costs of only $1.00 perunit, whereas labour-intensive firm B has fixed costs of only $15,000 per year, but its variablecost per unit is much higher at $3.00 per unit. Both firms produce and sell 10,000 widgets peryear at a price of $5.00 per widget.Firm A has a higher amount of operating leverage because of its higher fixed costs, but firm Aalso has a higher breakeven point
 — 
the point at which total costs equal total sales. Nevertheless,a change of Ipercent in sales causes more than a I percent change in operating profits for firm A,
 but not for firm B. The ―degree of operating leverage‖ measures this effect. The following
simplified equation demonstrates the type of equation used to compute the degree of operatingleverage, although to calculate this figure the equation would require several additional factorssuch as the quantity produced, variable cost per unit, and the price per unit, which are used todetermine changes in profits and sales: 
Operating leverage is a double-edged sword, however. If firm A’s sales decrease by I percent, its
profits will decrease by more than I percent, too. Hence, the degree of operating leverage showsthe responsiveness of profits to a given change in sales.
Implications:
Total risk can be divided into two parts: business risk and financial risk. Business
risk refers to the stability of a company’s assets if it uses no debt or preferred stock financing.
Business risk stems from the unpredictable nature of doing business, i.e., the unpredictability of consumer demand for products and services. As a result, it also involves the uncertainty of long-term profitability. When a company uses debt or preferred stock financing, additional risk 
 — 
financial risk 
 —is placed on the company’s common shareholders. They
demand a higher
expected return for assuming this additional risk, which in turn, raises a company’s costs.
Consequently, companies with high degrees of business risk tend to be financed with relativelylow amounts of debt. The opposite also holds: companies with low amounts of business risk canafford to use more debt financing while keeping total risk at tolerable levels. Moreover, usingdebt as leverage is a successful tool during periods of inflation. Debt fails, however, to provideleverage during periods of deflation, such as the period during the late 1990s brought on by theAsian financial crisis.

Q4. What are the factors that affect the financial plan of a company?
A4. To help your organization succeed, you should develop a plan that needs to be followed.This applies to starting the company, developing new product, creating a new department or anyundertaking that affects the company’s future. There are several factorsthat affect planning in anorganization. To create an efficient plan, you need to understand the factors involved in theplanning process.
Priorities
 In most companies, the priority is generating revenue, and this priority can sometimes interferewith the planning process of any project. For example, if you are in the process of planning alarge expansion project and your largest customer suddenly threatens to take their business toyour competitor, then you might have to shelve the expansion planning until the customer issueis resolved. When you start the planning process for any project, you need to assign each of theissues facing the company a priority rating. That priority rating will determine what issues willsidetrack you from the planning of your project, and which issues can wait until the process iscomplete.
Company Resources
 Having an idea and developing a plan for your company can help your company to grow andsucceed, but if the company does not have the resources to make the plan come together, it canstall progress. One of the first steps to any planning process should be an evaluation of theresources necessary to complete the project, compared to the resources the company hasavailable. Some of the resources to consider are finances, personnel, space requirements, accessto materials and vendor relationships

Forecasting
 A company constantly should be forecasting to help prepare for changes in the marketplace.Forecasting sales revenues, materials costs, personnel costs and overhead costs can help acompany plan for upcoming projects. Without accurate forecasting, it can be difficult to tell if the plan has any chance of success, if the company has the capabilities to pull off the plan and if the plan will help to strengthen the company’s standing within the industry. For example, if your forecasting for the cost of goods has changed due to a sudden increase in material costs, then thatcan affect elements of your product roll-out plan, including projected profit and the long-termcommitment you might need to make to a supplier to try to get the lowest price possible.
Contingency Planning
 To successfully plan, an organization needs to have a contingency plan in place. If the companyhas decided to pursue a new product line, there needs to be a part of the plan that addresses thepossibility that the product line will fail. The reallocation of company resources, the acceptablefinancial losses and the potential public relations problems that a failed product can cause allneed to be part of the organizational planning process from the beginning .


Q5. An employee of a bank deposits Rs. 30000 into his PF A/c at the end of each year for 20 years. What is the amount he will accumulate in his PF at the end of 20 years, if the rate of interest given by PF authorities is 9%? Hint Amount= 1534800
A.5
30000*FVIFA (9%, 20Y)
= 30000*51.160
= Rs. 1534800


Q6. Mr.Anant purchases a bond whose face value is Rs.1000, and which has a nominal interest rate of 8%. The maturity period is 5 years. The required rate of return is 10%. What is the price he should be willing to pay now to purchase the bond?
Hint: 924.28
A.6 
Interest payable=1000*8%=Rs. 80

Principal repayment is Rs. 1000

Required rate of return is 10%

V0=I*PVIFA(kd, n) + F*PVIF(kd, n)

Value of the bond=80*PVIFA(10%, 5y) + 1000*PVIF(10%, 5y)

= 80*3.791 + 1000*0.621

= 303.28 + 621

=Rs. 924.28
This implies that the company is offering the bond at Rs. 1000 but is worth Rs. 924.28 at the required rate of return of 10%. The investor may not be willing to pay more than Rs. 924.28 for the bond today.

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