Question

1- What is the copon rate of the bond given the information below. The bond makes semiannual interest payments. (Do not round intermediate calculations, round answer to two decimals, i.e. 32.16)

YTM:10.2%

Maturity (years):9

Current Price: $1,130.33

Par value: $1,000.00

Cpoupon Rate: ?

3- Question 7

5 Points

2- What is the price of the bond given the information below. The bond makes semiannual interest payments. (Do not round intermediate calculations, round answer to two decimals, i.e. 32.16)

Coupon Rate:6.1%

YTM:11.3%

Maturity (years):5

Par value: $2,000

Current Price: ?

3-  What is the price of the municipal bond given the information below. The bond makes semiannual interest payments. (Do not round intermediate calculations, round answer to two decimals, i.e. 32.16)

Coupon Rate:5.8%

YTM:6.9%

Maturity (years):17

Par value: $5,000

Current Price: ?

Answer 1

1) Here YTM = 10.2%/2 = 5.1%
n = no of coupon payments = 9 x 2 = 18
Current price = $ 1130.33
Face value = $1000
Interest = ?
YTM = Interest +(Face value -current market price/n) / (Face value + current market price/2)
= 5.1% = Interest +(1000-1130.33)/18 / (1000+1130.33)/2
5.1% = Interest +(-130.33/18) / 2130.33/2
5.1% = Interest -7.24 / 1065.17
5.1% x 1065.17= Interest - 7.24
= 54.32 = Interest - 7.24
= Interest = 61.56
Rate of interest = 61.56/1000 = 0.0616
i.e 6.16%
Annual rate = 6.16% x 2 =12.32%

2)

Here YTM = 11.3%/2 = 5.65%
n = no of coupon payments = 5 x 2 = 10
Current price = ?
Face value = $2000
Interest = 2000 x 6.1% x 1/2 = 61$

Value of bond = Interest x PVIFA(YTM%,n) + redemption value x PVIF(YTM%,n)
PVIFA(YTM%,n) = [1-(1/(1+r)^n / r ]
PVIFA(5.65%,10) = [1-(1/(1+5.65%)^10 / 5.65%]
=[1-(1/(1+0.0565)^10 / 0.0565]
=[1-(1/(1.0565)^10 / 0.0565]
=[1-0.57717 / 0.0565]
=0.42283/0.0565
=7.4837
PVIF(5.65%,10) = 1/(1+5.65%)^10
=1/(1.056)^10
= 0.57717
Value of bond = 61 x 7.4837 + 2000 x 0.57717
=456.5050 + 1154.3433
= 1610.85 $

3)

Here YTM = 6.9%/2 = 3.45%
n = no of coupon payments = 17 x 2 = 34
Current price = ?
Face value = $5000
Interest = 5000 x 5.8% x 1/2 = 145$

Value of bond = Interest x PVIFA(YTM%,n) + redemption value x PVIF(YTM%,n)
PVIFA(YTM%,n) = [1-(1/(1+r)^n / r ]
PVIFA(3.45%,34) = [1-(1/(1+3.45%)^34 / 3.45%]
=[1-(1/(1+0.0345)^34 / 0.0345]
=[1-(1/(1.0345)^34 / 0.0345]
=[1-0.31562 / 0.0345]
=0.68438/0.0345
=19.8371
PVIF(3.45%,34) = 1/(1+3.45%)^34
=1/(1.0345)^34
= 0.31562
Value of bond = 145 x 19.8371 + 5000 x 0.31562
=2876.38 + 1578.09
= 4454.48$