Question

Info

1. Current YTM = 8.5%

2. Liabilities at the end of 5 years = 10,000(1.085)^5 = 15,036.56

3. Buy the bond that has a coupon of 8%, YTM 8.5%, N = 5

Calculate -

1. Duration

2. Can you match duration of your liabilities?

3. Calculate what happens if your YTM rises by 1%

***please only answer question 2 [Can you match duration of your liabilities?]. i will post 3 after i get the answer for 2. i included them in case they were important.***

answer for part 1 - https://www.chegg.com/homework-help/questions-and-answers/info-current-ytm-85-liabilities-end-5-years-10-000-1085-5-15-03656-buy-bond-coupon-8-ytm-8-q30555163

Answer 1

1. Price of bond = 800 * PVAF ( 8.5 %, 5) + 10000 * PVIF ( 8.5 % , 5)

= 800 * 3.9406 + 10000 * 0.6650

= 3152.48 + 6550

= 9702.48

Current Yield = (Coupon Amount / Price) * 100

= (800 / 9702.48) * 100

                                              = 8.24 %

Duration of asset = { (Current Yield / Yield to maturity) * PVAF ( YTM, n)* (1 + ytm) } + { 1- (Current Yield / Yield to maturity) * n}

= { (8.24/ 8.5) * PVAF ( 8.5%, 5)* (1 .085) } +[ { 1- (8.24 / 8.5)} * 5]

= 4.14 + 0.15

= 4.29 years.

2) Duration of Liabilities =

Years (x) Liability PV@ 8.5%(w) wx

5 15036.56 10000 50000

10000 50000

Duration of Liabilities = 50000 / 10000 = 5 years.

So, the duration of Liabilities doesnot match duration of asset.