Alexander Smith and Olivia Williams are vice presidents of Mutual of Seattle Gro

Question

Alexander Smith and Olivia Williams are vice presidents of Mutual of Seattle Group Health Cooperative and co-directors of the organization's pension fund management division. The unions that represent the GHC hospital staff have requested an investment seminar so that they better understand the decisions being made on behalf of their members. Alexander and Olivia, who will make the actual presentation, have asked you to help them by answering the following questions.            

a. What is the value of a ten-year, $1,000 par value bond with a 10 percent annual coupon if its required rate of return is 10 percent?           

b. What would be the value of the bond described in question a. if, just after it had been issued, the expected inflation rate rose by 3 percentage points, causing investors to require a 13 percent return? Would we now have a discount or a premium bond?

c. What would be the value of the bond described in question a. if, just after it had been issued, the expected inflation rate fell by 3 percentage points, causing investors to require a 7 percent return? Would we now have a discount or a premium bond?                                                                                        

d. What would happen to the value of the ten-year bond over time if the required rate of return remained at 13 percent, remained at 7 percent, or remained at 10 percent?                                                               

Explanation / Answer

A) The value of the bond will remain same at $1000, as because the bond is paying coupon at the same rate of interest as compare to market, and so, when we calculate the Inflows using the DF@10%, we get the same value.

As we Know Value of a bond = PV of all the inflows, discounted at market value.

Value of a bond = Coupon Amount * PVaf(10%, 10Years)+Face value * PVif(10%, 10Years)

Value of a bond = $100 * 6.1446 + $1000 * 0.3854

Value of a bond = $1000.

Hence the value remain same only.

B) If the market requires 13%, the bond now have discount as becausse the market is expecting 13% and the bond is only giving 10% lower then market so the bond will have to compensate such lower interest rate by discounting it.

Hence the new value of bond will be,

As we Know Value of a bond = PV of all the inflows, discounted at market value.

Value of a bond = Coupon Amount * PVaf(13%, 10Years)+Face value * PVif(13%, 10Years)

Value of a bond = $100 * 5.4262 + $1000 * 0.2946

Value of a bond = $837.21

C)  If the market requires 7%, the bond now have premium as because the market is expecting 7% and the bond is giving 10% higher then market so the bond will ask premium for such higher interest rate.

Hence the value of Bond will be,

As we Know Value of a bond = PV of all the inflows, discounted at market value.

Value of a bond = Coupon Amount * PVaf(7%, 10Years) + Face value * PVif(7%, 10Years)

Value of a bond = $100 * 7.0236 + $1000 * 0.5083

Value of a bond = $1210.71

D) At 13%, Value of Bond will fall below to $837.21

At 7%, Value of Bond will increased to $1210.71

At 10%, the value of bond will remain same.

(All the calculation has been shown in part A,B&C itself)

If you understand the concept please hit the thumps up and if you have any doubt feel free to Comment. Keep Chegging

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