Question

1-

Formula problem:

Determine the market price of a 25-year, 5.25%, $150,000 coupon bond when the market interest rate is 5.75%.

2-

Formula Problem:

Determine the annual holding period rate of return on a 22-year, $90,000 discount bond that you originally purchased for $30,800 and sold 12 years later for $50,500.

* please For the formula problems, set up the problem and solve. Be sure to show each step

• Round all $ problems to the nearest dollar.
• All rate problems must be carried at least 4 decimal places and left in % form.
• Work must be shown and all answers must be legible

Answer 1

1. Computation of Market price of a bond:

Given

Face value = $ 150000

Coupon Rate = 5.25%

Market interest rate = 5.75%

Coupon Amount = Face value * Coupon rate

= $ 150000*5.25%

= $ 7875

Term to Maturity = 25 Years

We know that the Present value of Cashinflows at market rate of interest is equal to the Current price of the bond.

There are two types of cash inflows are associated with the bond. One is Coupon amount coming every year and the maturity amount at the end of 25 th year

Present value of Cash inflows = Interest accruing from year 1 to 25 + Maturity amount

Computation of Present value of interest

Present value of interest = Interest * PVAF ( 5.75%,25)

= $ 7875 * 13.0927

= $ 103105.0125

Computation of Present value of Maturity amount:

PV of Maturity amount = $ 150000* PVF ( 5.75%,25)

= $ 150000*0.2472

= $ 37080

Present value of Cash inflows = Interest accruing from year 1 to 25 + Maturity amount

= $ 103105.0125+ $ 37080

= $ 140185.0125

Hence the Current Market price of a bond is $ 140185.0125

2. Computation of Holding period return:

Purchase price of a bond = $ 30800

Sale price of a bond = $ 50500

Holding period = 12 Years

Holding period return = ( Sale price - Purchase price ) / Purchase price

= ( $ 50500- $30800) / $30800

= $ 19700/ $ 30800

= 0.639610

Hence Holding period is 63.9610%.

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