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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?

Answer :

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Answer:

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

The present value of Hersey's bond = $1125.513.

And, the present value of the Mars bond = $1172.259.

Calculation of the present value:

For Hersey bond;

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

Coupon (C) = $30

Rate (r) = 0.1 = 0.025(quarterly)

Pay at maturity(p) = $1000

Now the following formula should be used

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

For Mars bond;

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

Coupon (C) = $30

Rate (r) = 0.1 = 0.025(quarterly)

Pay at maturity(p) = $1000

Now

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

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