Question

1. Given the information below

Par value of coupon = $1000
Coupon payment = $45
Price = $ 910
Number of compounding periods = 30

Calculate Before Tax Cost of debt using formula not financial calculator.

Answer 1

PMT = Coupon; R = Rate = ?; FV = Face value; N = Number of period

Bond value or Price = PMT x ((1-((1+R)^-N)) / R) + (FV/(1+R)^N)

We will do trial and error to get the Yield or YTM:

Step 1:

Let’s discount the bond with 4.75% (random rate)

Bond value = 45 x ((1-((1+4.75%)^-30)) /4.75%) + 1000/(1+4.75%)^30)

Bond value = BV = $960.45

Step 2:

Let’s discount the bond with 5% ( again random rate)

Bond value = BV = 45 x ((1-((1+5%)^-30)) /5%) + 1000/(1+5%)^30)

Bond value = $923.14

Step 4:

Difference between two Bond values = 960.45-923.14 = $37.31

Difference in two discount rate = 0.25%

Step 5:

Real YTM = Lower random rate + Difference in two discount rate x (BV at 4.75% - Current market value)/Difference between two Bond values

Real YTM = 4.75% + 0.25% x (960.45 - 910)/37.31

Real YTM = 5.09%

Seems to be close

Using financial calculator BA II Plus - Input details:	#
FV = Future Value / Face Value =	-$1,000.00
PV = Present Value =	$910.00
N = Number of years remaining x frequency =	30
PMT = Payment = Coupon / frequency =	-$45.00
CPT > I/Y = Rate = YTM =	5.091590
Convert rate in yearly rate =	5.09%