B6005 Financial Management

Answer Key In-class Exercise 3 Bond Valuation

Discounted cash flows                                                                                         Answer: F

.         The market value of any real or financial asset, including stocks, bonds, or art work, may be found by determining future cash flows and then discounting them back to the present.

Call provision                                                                                                                  Answer: F 

.       A call provision gives bondholders the right to demand, or "call for," repayment of a bond.  Typically, calls are exercised if interest rates rise, because when rates rise the bondholder can get the principal amount back and reinvest it elsewhere at higher rates.

Bond value                                                                                                                       Answer: T 

.     If the required rate of return on a bond is greater than its coupon interest rate (and k_d remains above the coupon rate), the market value of that bond will always be below its par value until the bond matures, at which time its market value will equal its par value.  (Accrued interest between interest payment dates should not be considered when answering this question.)

Bond ratings and required returns                                                                               Answer: T 

.       There is an inverse relationship between bond ratings and the required return on a bond.  The required return is lowest for AAA-rated bonds, and required returns increase as the ratings get lower.

Bond value - annual payment                                                                                                         

.         You have just noticed in the financial pages of the local newspaper that you can buy a $1,000 par value bond for $800.  If the coupon rate is 10 percent, with annual interest payments, and there are 10 years to maturity, should you make the purchase if your re­quired return on investments of this type is 12 percent?

Time Line:

      0    12%     1                               2                  3…………            9                10    Years

                  ├────────┼─────────┼─────────┼──────···─────┼───

            PMT = 100                        100               100                        100             100

 PV = ?                                                                                                               FV = 1,000

Numerical solution:

V_B       = $100(PVIFA_12%,10) + $1,000(PVIF_12%,10)

   = $100((1-  1/1.12¹⁰)/0.12) + $1,000(1/1.12¹⁰)

     = $100(5.6502) + $1,000(0.3220) = $887.02.

Thus, the value is significantly higher than the market price and the bond should be purchased.

Financial calculator solution:

Inputs: N = 10; I = 12; PMT = 100; FV = 1,000.  Output: PV = -$887.00.

Bond value - semiannual payment                                                                                                  

.       You intend to purchase a 10-year, $1,000 face value bond that pays interest of $60 every 6 months.  If your nominal annual required rate of return is 10 percent with semiannual compounding, how much should you be willing to pay for this bond?

Numerical solution:

V_B    = $60(PVIFA_5%,20) + $1,000(PVIF_5%,20)

     = $60((1-  1/1.05²⁰)/0.05) + $1,000(1/1.05²⁰)

= $60(12.4622) + $1,000(0.3769) = $1,124.63.

Financial calculator solution:

Inputs: N = 20; I = 5; PMT = 60; FV = 1,000.

Output: PV = -$1,124.62; V_B = $1,124.62.

Bond value - semiannual payment                                                                                                  

.     Assume that you wish to purchase a 20-year bond that has a maturity value of $1,000 and makes semiannual interest payments of $40.  If you require a 10 percent nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?

Numerical solution:

V_B = $40((1-  1/1.05⁴⁰)/0.05) + $1,000(1/1.05⁴⁰)

  = $40(17.1591) + $1,000(0.1420) = $828.36 » $828.

Financial calculator solution:

Inputs: N = 40; I = 5; PMT = 40; FV = 1,000. 

Output: PV = -$828.41; V_B » $828.

8. Assume that you are considering the purchase of a $1,000 par value bond that pays interest of $70 each six months and has 10 years to go before it matures.  If you buy this bond, you expect to hold it for 5 years and then to sell it in the market.  You (and other investors) currently require a nominal annual rate of 16 percent, but you expect the market to require a nominal rate of only 12 percent when you sell the bond due to a general decline in interest rates.  How much should you be willing to pay for this bond?

Answer

This involves solving for the value of bond at 2 stages.

First stage: solve for the value of bond at the time you sell it. The required rate of return is 12% per year.

Second stage: Once you know how much you can sell it for, you can find the bond price that you are willing to pay, with a required rate of return of 16% per year.

Numerical solution:

  V_B5    = $70(PVIFA_6%,10) + $1,000(PVIF_6%,10)

           = $70((1-  1/1.06¹⁰)/0.06) + $1,000(1.06¹⁰)

= $70(7.3601) + $1,000(0.5584) = $1,073.61.