Question

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SHOW ALL WORK PLEASE!! Sheel Inc. has 7 percent annual coupon (compounded semiannually) bonds on the...

SHOW ALL WORK PLEASE!!

Sheel Inc. has 7 percent annual coupon (compounded semiannually) bonds on the market with 22 years to maturity, and the par value of $1,000. At what price should the bonds be selling for if YTM is 5%? Had the bond been selling at $983.55, what would be the YTM (assuming the same coupon, maturity and par value)? Based on your answers above, what is the relationship between YTM and bond price?

Expert Solution

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using PV function in Excel :

rate = 5%/2 (Semiannual YTM of bonds = annual YTM / 2)

nper = 22 * 2 (22 years remaining until maturity with 2 semiannual coupon payments each year)

pmt = -1000 * 7% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = -1000 (face value receivable on maturity)

PV is calculated to be $1,265.04

YTM is calculated using RATE function in Excel with these inputs :

nper = 22 * 2 (22 years remaining until maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 7% / 2 (semiannual coupon payment = face value * coupon rate / 2)

pv = -983.55 (Current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1000 (face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

The RATE calculated is the semiannual YTM. To calculate the annual YTM, we multiply by 2.

Annual YTM is 7.15%

The relationship between bond price and YTM is :

Higher the YTM, lower the bond price
Lower the YTM, higher the bond price
If YTM > coupon rate, bond price < par value of bond
If YTM < coupon rate, bond price > par value of bond

jeff jeffy answered 2 years ago

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