Question

In: Finance

A GoodCredit company issued a bond with par value of $1,000.00, a time to maturity of...

A GoodCredit company issued a bond with par value of $1,000.00, a time to maturity of 15.00 years, and a coupon rate of 7.90%. The bond pays interest annually. If the current market price is $790.00, what will be the approximate capital gain on this bond over the next year if its yield to maturity remains unchanged? NOTE: Capital gain is change in bond price. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Solutions

Expert Solution

To solve this problem we will calculate YTM first, using the YTM we will calculate the price of the bond one year later to find the gain on the bond

Yield to maturity is the rate of return the investor will get if he/she hold the bold till maturity period

So YTM is like internal rate of return, if we discount all the cash inflow from the bond using YTM, the present value will be equal to the bond current price.

YTM is calculated using Excel, the function used is (IRR)

Pls refer below table

Year

Cash flow

Amount

0

Bod price (Outflow)

-790

1

Coupon (Inflow)

79

2

Coupon (Inflow)

79

3

Coupon (Inflow)

79

4

Coupon (Inflow)

79

5

Coupon (Inflow)

79

6

Coupon (Inflow)

79

7

Coupon (Inflow)

79

8

Coupon (Inflow)

79

9

Coupon (Inflow)

79

10

Coupon (Inflow)

79

11

Coupon (Inflow)

79

12

Coupon (Inflow)

79

13

Coupon (Inflow)

79

14

Coupon (Inflow)

79

15

Par + Coupon (Inflow

1079

YTM

10.79%

Formula used = IRR

IRR will not change after one year so after one year the price of the bond will be

Price of the bond could be calculated using below formula.

P = C* [{1 - (1 + YTM) ^ -n}/ (YTM)] + [F/ (1 + YTM) ^ -n]

Where,

                Face value = $1000

                Coupon rate = 7.9%

                YTM or Required rate = 10.79%

                Time to maturity (n) = 14 years

                Annual coupon C = $79

Let's put all the values in the formula to find the bond current value

P = 79* [{1 - (1 + 0.1079) ^ -14}/ (0.1079)] + [1000/ (1 + 0.1079) ^14]

P = 79* [{1 - (1.1079) ^ -14}/ (0.1079)] + [1000/ (1.1079) ^14]

P = 79* [{1 - 0.23823}/ 0.1079] + [1000/ 4.19767]

P = 79* [0.76177/ 0.1079] + [238.2274]

P = 79* 7.05996 + 238.2274

P = 557.73684 + 238.2274

P = 795.96424

So price of the bond is $795.96

The bond was purchased at 790 and after one year it is sold at 795.96 so total gain is $5.96

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Feel free to comment if you need further assistance J

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