Question

BACKGROUND: The Company is issuing 10,000 bonds, each with a face value of $975, a stated rate of 8.5%, and a 20-year term. When the bonds are issued, the market rate is 7.1%. REQUIRED:

a) What is the maximum price an investor will pay for a single bond? b) What is the total amount of capital collected by the Company if all of the investors pay the maximum price?

BACKGROUND: 8 years later, an investor sells his bond for $950. REQUIRED:

c) What is the actual yield to maturity (YTM)? d) If the YTM were 8.1%, what would be the current price?

Answer 1

a]

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 = 7.1% (YTM of bonds = market interest rate)

nper = 20 (Years remaining until maturity with 1 coupon payment each year)

pmt = 975*8.5% (annual coupon payment = face value * coupon rate)

fv = 975 (face value receivable on maturity)

PV is calculated to be $1,118.49

А1 X fc =PV(7.1%,20,975*8.5%,975) B C D 1 ($1,118.49)!

The maximum price is $1,118.49

b]

total amount of capital collected = price per bond * number of bonds issued

total amount of capital collected = $1,118.49 * 10,000 = $11,184,911.42

c]

Actual YTM is calculated using RATE function in Excel :

nper = 8 (number of years the bond is held, with 1 coupon payment each year)

pmt = 975*8.5% (annual coupon payment = face value * coupon rate)

pv = -1118.49 (Price paid to purchase bond. This is entered with a negative sign because it is a cash outflow to the buyer of the bond)

fv = 950 (price at which bond is sold at end of 8 years)

RATE is calculated to be 5.88%. This is the actual yield earned by the investor

| A2 X foc =RATE(8,975*8.5%,A1,950) B C D E F ($1,118.49) 5.88%

d]

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 = 8.1% (YTM of bonds)

nper = 12 (Years remaining until maturity with 1 coupon payment each year)

pmt = 975*8.5% (annual coupon payment = face value * coupon rate)

fv = 975 (face value receivable on maturity)

PV is calculated to be $1,004.24

A3 X fac =PV(8.1%,12,975*8.5%,975) в с D E F 3 ($1,004.24)!

The current price would be $1,004.24