can someone give me the Written formula used to solve question #1 and #2 In this

Question

can someone give me the Written formula used to solve question #1 and #2

In this part of the assignment, you will:

1.Determine the value of bonds paying annual and semiannual interest payments

2.Determine the yield to maturity of bonds paying annual and semiannual interest payments

Bonds

1. Bond. What is the value of a $1,000 par value bond with annual payments of an

a. 10% coupon with a maturity of 10 years and a 15% required return? $749.06

b. 8% coupon with a maturity of 10 years and a 8% required return? $1,000.00

c. 11% semiannual coupon with a maturity of 20 years and a 11% required return? $1,000.00

d. 8% semiannual coupon with a maturity of 20 years and a 9% required return? $907.99

2. Bond. What is the yield to maturity of a $1000 par value bond with an

a. 10% annual coupon and 10 years to maturity and a $1,000 price? 10%

b. 9.5% annual coupon and 20 years to maturity and a $788 price? 12.41%

c. 5.0% annual coupon and 8 years to maturity and a $800 price? 8.55%

Explanation / Answer

Part 1)

The formula for calculating the value of bonds with the use of information provided in the question is:

Present/Current Value of Bonds = Annual Interest Payment*PVIFA(r,n) + Face Value*PVIF(r,n) where r= Required Return, n = Period, PVIFA = Present Value Interest Factor for an Annuity and PVIF = Present Value Interest Factor

The value of PVIFA and PVIF can be obtained from the respective Present Value Tables. You need to look for the relevant return percentage and use the present value for the years.

For Instance, for part a) the formula would be 1,000*10%PVIFA(15%,10 Years) + 1,000*PVIF(15%,10) Years. The PVIFA and PVIF value for 15% for a period of 10 years would be 5.0188 and .2472. Using these values in the above equation, we get,

Value of Bond = 100*5.0188 + 1,000*.2472 = $749.08

Similarly, this formula can be used for other parts, the equarions are given below:

b) Value of Bond = 1,000*8%*PVIFA(8%,10) + 1,000*PVIF(8%,10)

c) Value of Bond = 1,000*11%*1/2*PVIFA(5.5%,40) + 1,000*PVIF(5.5%,40) [since bond is semi-annual, we divide rate by 2 and multiply period by 2]

d) Value of Bond = 1,000*8%*1/2*PVIFA(4.5%,40) + 1,000*PVIF(4.5%,40) [since bond is semi-annual, we divide rate by 2 and multiply period by 2]

_________________

Part 2)

The best way to calculate YTM is with the use of Rate function/formula of EXCEL/Financial Calculator. The function/formula for YTM is Rate(Nper,PMT,-PV,FV) where Nper = Period, PMT = Interest Amount, PV = Present Value and FV = Face Value. The equation for the cases provided in the question would be as follows:

a) Rate(10,100,-1000,1000)

b) Rate(20,95,-788,1000)

c) Rate(8,50,-800,1000)

Another way would be would to calculate YTM would be the use of following equations:

a) 1,000 (Current Value of Bond) = 1,000*10%*PVIFA(r,10) + 1,000*PVIF(r,10)

b) 788 (Current Value of Bond) = 1,000*9.5%*PVIFA(r,20) + 1,000*PVIF(r,20)

c) 800 (Current Value of Bond) = 1,000*5%*PVIFA(r,8) + 1,000*PVIF(r,8)

In the above equations, r will be calculated with the use of trial and error method with the use of different interest rates. PVIFA and PVIF tables will have to be referred to for various interest rates keeping in view the period.

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