Question

Applying Time Value of Money Concepts
Complete the missing information in the table below. Assume that all bonds pay interest semiannually.

Do not use negative signs with answer.
Round percentages to one decimal place (ex. 0.0345 = 3.5%).
Round all other values to the nearest whole number.

	Annual	Years to	Coupon		Issue
	Yield	Maturity	Rate	Face value	Proceeds
Firm 1	8.00%	15	7.00%	$200,000
Firm 2	3.00%	10	0.00%		$334,112
Firm 3	6.50%		5.00%	$500,000	$473,952
Firm 4		12	3.50%	$1,000,000	$1,125,213
Firm 5	0.80%	20	2.00%	$400,000

Answer 1

Solution :

Firm 1:

Annual yield = 8%

Coupon rate = 7%

Maturity = 15 years

Face value = $200,000

Issue proceed = Present value of cash flows discounted at 8% annual yield

= ($200,000*3.50%)*cumulative PV factor at 4% ofr 30 periods + $200,000 * PV Factor at 30 periods at 4%

= ($7,000 * 17.29203) + ($200,000*0.308319) = $182,708

Firm 2:

Annual yield = 3%

Coupon rate = 0%

Maturity = 10 years

Issue price = $334,112

Let face value of bond is x. Face value is the maturity amount after 10 years, therefore

$334,110 * (1+0.015)^20 = X

X = $450,000

Firm 3:

Annual yield = 6.50%

Coupon rate = 5%

Face value = $500,000

Issue price = $473,952

let maturity period is t, hence there are 2t semi annual period.

Now present value of future cash flows discounted at 6.50% will be equal to issue price of bond

Therefore

($500,000*2.50%)*cumulative PV factor at 3.25% for 2t periods + $500,000* PV factor at 3.25% at 2t period = $473,952

If we calculate present value at 10 periods then

$12,500 * 6.94624 + $500,000* 0.774247 = $473,952

Hence 2t = 10

t = 5

Therefore maturity period is 5 years.

Firm 4:

Face Value = $1,000,000

Issue price = $1,125,213

Coupon rate = 3.50%

Maturity period = 12 years

Let semiannual yield is i, therefore annual yield is 2i

Now

($1,000,000*1.75%) * cumulative PV Factor at i rate for 24 periods + $1,000,000 * PV factor at i rate at 24 period = $1,125,213

Let calculate Present value of future cash flows at 1.15% semiannual rate

= $17,500*20.86879 + $1,000,000*0.760009 = $1,125,213

hence i = 1.15%

Therefore annual yield = 1.15*2 = 2.30%

Firm 5:

Annual yield = 0.80%

Coupon rate = 2%

Maturity = 20 years

Face value = $400,000

Issue proceed = Present value of cash flows discounted at 0.80% annual yield

= ($400,000*1%)*cumulative PV factor at 0.40% for 40 periods + $400,000 PV factor at 0.40% at 40 periods

= ($4,000*36.89605) + ($400,000*0.852416) = $488,551