Question

BOND VALUATION FINANCE

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.

Need Equation For All Answers

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

For all questions, assume a par value is $1,000 and semiannual bond interest payments.

a) Issued at Par bonds with a coupon rate of 5.8% and a maturity of twenty years.

We need to find the yield to maturity.

The YTM is the rate at which

Current Price of Bond = All future cash flows discounted at YTM

We will use excel function of Rate to find the value (The same logic can be used in a financial calculator)

Here,

Time to maturity = NPER = 20 years = 20 x2 = 40 Half years (As coupons are paid semi annually)

Coupons = PMT = 1000 x 5.8% /2 = $29 (Semi annual coupons, so $29 received 40 times during the life of bond)

Issue price of Bond = PV = - $1000 (Bonds are issued at par, the negative indicates to excel that this is a cash outflow)

Maturity price of bond = FV = $1000 (Amount received at maturity)

Type = 0 (Since coupons are paid at the end of period. In excel 0 is used to indicate, amount paid at end & 1 is used if amount paid beginning

Using Rate function in excel

Rate = Rate(40,29,-1000,1000,0) =2.90%

This is half year rate,

Annual Rate = 2.90% x 2 = 5.80%

The Bond equation for above

1000 = 29 x PVIFA(40,r/2 %) + 1000 PVIF(40,r/2 %)

PVIFA = (1 - (1 + r)^-n) / r, where r is periodic interest rate & n is number of payments

PVIF = 1/ (1+r)^n

b. Outstanding bond issue with a coupon of 8% which will mature in five years. The bond now sells for $1,141.69.

Again we will use rate function

Here, NPER = 5 x2 = 10 half years, PMT = 1000 x 8%/2 = $40, Purchase price = PV = -1141.69, FV = 1000, Type =0

Rate = Rate(10,40,-1141.69,1000,0)

= 2.39%

This is half year rate,

Annual Rate = 2.39% x 2 = 4.78%

The Bond equation for above

1141.69 = 40 x PVIFA(10,r/2 %) + 1000 PVIF(10,r/2 %)

PVIFA = (1 - (1 + r)^-n) / r, where r is periodic interest rate & n is number of payments

PVIF = 1/ (1+r)^n

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?

For Bond to have a current price close to (equal to) Par value, the coupon rate should be equal to Yield to Maturity of the bond.

For a, it should be 5.8% annual (as it is)

For B, we will check with PMT function

Rate = YTM = 2.39% , NPER = 10, PV = -1000, FV = 1000, Type = 0

PMT = PMT(2.39%,10,-1000,1000,0)

= $23.90 (per period or per half year)

Coupon Rate = Coupon x 2 (2 coupons in a year) / Bond Price

= 23.90 x 2 /1000 = 4.78%

The Bond equation for above

1000 = Z x PVIFA(10,2.39%) + 1000 PVIF(10,2.39%)

PVIFA = (1 - (1 + r)^-n) / r, where r is periodic interest rate & n is number of payments

PVIF = 1/ (1+r)^n

where Z = Coupon (Half yearly)

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%?

Here, we will first find the YTM of bond, and then change the YTM to desired level to find the price of bond

Since, Grace wants to sell it at Par, the coupon rate = YTM of the bond (As seen in above question)

1) Now if the yield drops to 5%, the price of bond will change

Here, Rate = 5%/2 = 2.5%, NPER = 20 x 2 = 40, PMT = 6%/2 x 1000 = $30, FV = 1000, Type =0

Price of Bond is to be found using PV

PV = PV(2.5%,40,30,1000,0)  = - $1125.51

The Bond equation for above

Price = 30 x PVIFA(40,2.5%) + 1000 x PVIF(40,2.5%)

PVIFA = (1 - (1 + r)^-n) / r, where r is periodic interest rate & n is number of payments

PVIF = 1/ (1+r)^n

2) Now if the yield goes up to 7%, the price of bond will change

Here, Rate = 7%/2 = 3.5%, NPER = 20 x 2 = 40, PMT = 6%/2 x 1000 = $30, FV = 1000, Type =0

Price of Bond is to be found using PV

PV = PV(3.5%,40,30,1000,0)  = - $893.22

The Bond equation for above

Price = 30 x PVIFA(40,3.5%) + 1000 x PVIF(40,3.5%)

PVIFA = (1 - (1 + r)^-n) / r, where r is periodic interest rate & n is number of payments

PVIF = 1/ (1+r)^n

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)

Number of bonds of $1000 issued in $50 Million = 50,000,000/ 1000 = 50,000

1. If Yield is 5%,

Money realized by Grace = Bond Price X Number of bonds

= 1125.51 x 50000 (From question d)

= $56.28 Million

2. If Yield is 7%,

Money realized by Grace = Bond Price X Number of bonds

= $ 893.22 x 50000 (From question d)

= $44.66 Million