Chapter 5: Q16BP (page 530)

A $1,000 par value bond was issued 20 years ago at a 9 percent coupon rate. It currently has 5 years remaining to maturity. Interest rates on similar debt obligations are now 10 percent.
a. Compute the current price of the bond using an assumption of semiannual payments.
b. If Mr. Robinson initially bought the bond at par value, what is his percentage loss (or gain)?
c. Now assume Mrs. Pinson buys the bond at its current market value and holds it to maturity, what will her percentage return be?
d. Although the same dollar amounts are involved in parts b and c, explain why the percentage gain is larger than the percentage loss.

Short Answer

Expert verified

Answer

(a) The current price of a bond is $961.39

(b) The percentage of loss is computed as 3.861%

(d) The difference is because of the price of the bond.

Step by step solution

Computation of bond value

$C o u p o n (C) = F a c e V a l u e \times C o u p o n R a t e = 1, 000 \times \frac{9 %}{2} = $ 45$

$B o n d V a l u e = C \times \frac{[1 - \frac{1}{{(1 + r)}^{r}}]}{r} + \frac{F}{(1 + r)} = 45 \times \frac{[1 - \frac{1}{{(1 + 0.05)}^{10}}]}{0.05} + \frac{1, 000}{{(1 + 0.05)}^{10}} = $ 961.3913$

Computation of percentage gain or loss

$P r o f i t o r L o s s = S e l l i n g p r i c e - P u r c h a s e P r i c e = 961.39 - 1, 000 = - 38.61$

$P e r c e n t a g e o f l o s s = \frac{L o s s}{P u r c h a s e d P r i c e} \times 100 = \frac{- 38.61}{1, 000} \times 100 = 3.861 %$

Computation of profit percentage return

In this case, bonds are held till maturity which indicates that the selling price will be equal to the par value of the bond. Therefore, the selling price will be $1,000

$P r o f i t o r L o s s = S e l l i n g p r i c e - P u r c h a s e P r i c e = 1, 000 - 961.39 = $ 38.61$

$P e r c e n t a g e o f l o s s = \frac{Loss}{Purchased Price} \times 100 = \frac{38.61}{961.39} \times 100 = 4.01 %$

Reason for a greater percentage gain than the percentage loss

The Reason for the variation in gain and loss is because of the price of the bonds in part B the bond price is $1,000 but in part C the bond price is $961.39.

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Short Answer

Step by step solution

Computation of bond value

Computation of percentage gain or loss

Computation of profit percentage return

Reason for a greater percentage gain than the percentage loss

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