Question

ScanSoft Development Company is developing

a new process to manufacture optical disks.

The development costs were higher than

expected, so ScanSoft required an immediate

cash inflow of $5 200 000. To raise the required

capital, the company decided to issue bonds.

Since ScanSoft had no expertise in issuing and

selling bonds, the company decided to work

with an investment dealer. The investment

dealer bought the company's entire bond issue

at a discount, and then planned to sell the

bonds to the public at face value or the current

market value. To ensure it would raise the $5

200 000 it required, ScanSoft issued 5200

bonds with a face value of $1000 each on

January 20,2016. Interest is paid semi-annually

on July 20 and January 20, beginning July 20,

2016. The bonds pay interest at 5.5%

compounded semi-annually

ScanSoft directors realize that when the bonds

mature on January 20, 2036, there must be $5

200 000 available to repay the bondholders. To

have enough money on hand to meet this

obligation, the directors set up a sinking fund

using a specially designated savings account.

The company earns interest of 1.6%

compounded semi-annually on this sinking fund

account. The directors began making semi

annual payments to the sinking fund on July 20,

2016

ScanSoft Development Company issued the

bonds, sold them all to the investment

dealer, and used the money raised to continue

its research and development.

QUESTIONS

1. How much would an investor have to pay for

one of these bonds to earn 4.4%

compounded semi-annually?

2. (a) What is the size of the sinking fund

payment?

b) What will be the total amount deposited into

the sinking fund account would be by January

2036?

c) How much of the sinking fund will be

interest?

3. Suppose ScanSoft discovers on January 20,

2026, that it can earn 2.5% interest

compounded semi-annually on its sinking fund

account

a) What is the balance in the sinking fund after

the January 20, 2026, sinking fund payment?

b) What is the new sinking fund payment if the

fund begins to earn 2.5% on January 21, 2026?

c) What will be the total amount deposited into

the sinking fund account over the life of the bonds?

Answer 1

1]

The amount paid for the bond to earn 4.4% yield (YTM) compounded semiannually is calculated using PV function in Excel :

rate = 4.4% / 2 (converting annual rate into semiannual rate)

nper = 20 * 2 (total number of semiannual coupon payments = number of years * 2)

pmt = 1000 * 5.5% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value of bond receivable on maturity)

PV is calculated to be $1,145.31

2]

a]

Size of sinking fund payment is calculated using PMT function in Excel :

rate = 1.6% / 2 (converting annual rate earned on sinking fund into semiannual rate)

nper = 20 * 2 (total number of payments into sinking fund = number of years * 2)

pv = 0 (beginning amount in sinking fund is zero)

fv = 5,200,000 (ending amount required in sinking fund is $5.2 million)

PMT is calculated to be $110,822.36

b]

Total amount deposited into sinking fund = monthly deposit * total number of deposits = $110,822.36 * 40 = $4,432,894.51

c]

Amount of interest = ending value of sinking fund - Total amount deposited into sinking fund = $5,200,000 - $4,432,894.51 = $767,105.49