Leigh Delight Candy, Inc. is choosing between two bonds in which to invest their cash. One is being offered from Hershey's and will mature in 10 years and pay $30 each quarter. The other alternative is a Mars' bond that will mature in 20 years and pay $30 each quarter. What would be the present value of each bond if the discount rate is 10% compounded quarterly, and each bond pays $1,000 at maturity?

Hersey's bond = $1125.513

Mars bond = $1172.259

Explanation:

Hersey bond;

Period (t) = 10years = 40 (quartely)

Coupon (C) = $30

Rate (r) = 0.1 = 0.025 (quarterly)

Pay at maturity (p) = $1000

Using the both present value (PV) and compound interest formula;

PV = [ C * (1 - (1+r) ^-t) : r] + [p : (1 + r) ^t]

PV = [30 * (1 - (1.025) ^-40) : 0.025] + [1000: (1.025) ^40]

PV = (753.083251562) + (372.4306236)

PV = $1125.513

Mars bond;

Period (t) = 20years = 80 (quartely)

Coupon (C) = $30

Rate (r) = 0.1 = 0.025 (quarterly)

Pay at maturity (p) = $1000

PV = [ C * (1 - (1+r) ^-t) : r] + [p : (1 + r) ^t]

PV = [30 * (1 - (1.025) ^-80) : 0.025] + [1000: (1.025) ^80]

PV = (1033.55451663) + (138.704569467)

PV = $1172.259