QUESTION $3-$ BOND VALUATION

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 Aal 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 $5\mathrm{.}8\%$ and a maturity of twenty years. Moody's rated the bonds Aa$1$ 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\mathrm{.}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 $C$ and ignore selling costs.