Question

Grace Kennedy Limited is a leading producer of cranberry juice, canned cranberry sauce, fresh
berries, and sweetened dried cranberries, with production and processing facilities in St.
Catherine. Sales of traditional products such as fresh berries and canned cranberry sauce have
been declining for a long time; the fastest-growing products have been juices and dried fruit,
especially “light” and sugar-free juices.
Industry-sponsored advertising has highlighted research showing that cranberries are rich
in antioxidants and other phytonutrients that may protect against heart disease, cancer, stomach
ulcers, gum and urinary tract infections, and even such age-related afflictions as loss of
coordination and memory. These trends confirm the marketing department’s belief that Grace
should aggressively pursue the same health-conscious consumers who purchase certified organic
products.
Grace executives have now decided to introduce an organic line of products, starting with
juice and blended juice. This new line will become the company’s highest strategic priority for
the next two years. The introduction of certified organic products will be expensive. Preliminary
estimates indicate that Grace will need to invest $80 million in production and processing
facilities. The company hopes to finance the expansion by using $30 million of its own liquid
assets and $50 million in new debt in the form of bonds with a maturity of twenty years. Grace
expects the bonds to receive a rating of Aa1 or better from Moody’s.

For all questions, assume a par value is $1,000 and semiannual bond interest payments.
a) A company like Grace Kennedy recently issued at par bonds with a coupon rate of 5.8%
and a maturity of twenty years. Moody’s rated the bonds Aa1 and Standard & Poor’s
awarded them AA. What rate of return (yield to maturity) did investors require on these
bonds if the bonds are sold at par value?

b) Grace has one outstanding bond issue with a coupon of 8% which will mature in five
years. The bond now sells for $1,141.69. What is the yield to maturity on these bonds?

c) Based on your answers to Questions 1 and 2, what coupon rate should Grace offer if it
wants to realize $50 million from the bond issue and to sell the bonds as close to par
value as possible?

d) Suppose Grace offers a coupon rate of 6% on its twenty-year bonds, expecting to sell the
bonds at par. What will happen to the price of a single bond with a par value of $1,000 if
the required bond yield unexpectedly falls to 5% or rises to 7%?

e) How much money will Grace realize from its $50 million bond issue if the actual yield is
either 5% or 7%? (Hint: Refer to your answers to part d).

Answer 1

a)

Since the bond is issued and redeemed at par, the bond YTM is equal to the coupon rate

Hence, rate of return (yield to maturity) investors require = 5.8%

b)

We find the YTM of the bond

Using a financial calculator, we input the following

N = 10 ( Since there are 5 years and 5*2 = 10semi-annual periods)

PMT = 40( Since 8%/2 = 4% is the semi-annual coupon)

PV = 1,141.69 ( Bonds are sold at par value)

FV = 1000 ( Par value)

CPT I/Y, we get

I/Y = 2.39%

YTM = 2*I/Y = 2*2.39% = 4.78%

Hence the YTM on the bond = 4.78%

Approximate YTM without the use of financial calculator

Approx YTM per period =

where C is the coupon payment

F is the face value and P is the price

Yield per period = (40-141.69/10)/(2141.69/2) = 0.024

Approx YTM = 2*0.024 = 0.048 = 4.8%

c)

The YTM on the bond = 4.78%

If Grace wants to sell the bonds as close to par value as possible it should offer a coupon rate = YTM.

Hence, the coupon rate should be 4.78%

d)

If the bond yield falls to 5%

Using a financial calculator, we input the following

N = 40 ( Since there are 20 years and 20*2 = 40 semi-annual periods)

PMT = 30 ( Since 6%/2 = 3% is the semi-annual coupon)

I/Y = 2.5 ( YTM is 5%, hence yield per period is 5%/2 = 2.5%)

FV = 1000 ( Par value)

CPT PV, we get

PV = -1125.5138

Hence the bond price is $1125.5138

Bond price without Calculator

Bond price =

Bond price = (30*(1-(1+0.025)^(-40))/0.025) + (1000/(1.025^40))

Bond price = $1125.51

If the bond yield rises to 7%

Using a financial calculator, we input the following

N = 40 ( Since there are 20 years and 20*2 = 40 semi-annual periods)

PMT = 30 ( Since 6%/2 = 3% is the semi-annual coupon)

I/Y = 3.5 ( YTM is 7%, hence yield per period is 7%/2 = 3.5%)

FV = 1000 ( Par value)

CPT PV, we get

PV = -893.2246

Hence the bond price is $893.2246

Without using a calculator

Bond price =

Bond price = (30*(1-(1+0.035)^(-40))/0.035) + (1000/(1.035^40))

Bond price = $893.22

e)

$50 million is the amount when Bonds are sold at par value

If the actual yield is 5% ,the bond price is $1125.5138

Amount realized = (1125.5138/1000)*$50 million = $56.27569 million

If the actual yield is 7%,the bond price is $893.2246

Amount realized = (893.2246/1000)*$50 million = $44.66123million