Question

Ann and Suzan are classmates who graduated with business degrees from Athabasca University. Ann inherited $50,000 from her father. She considers forming a 10-year business partnership with Suzan. To join the partnership, Ann needs to invest $50,000. She believes her portion of the partnership will generate the following profits at a discount rate of 4%.

Year	Profits	Present Value
1	$2000
2	$4,000
3	$6,000
4	$7,000
5	$8,000
6	$10,000
7	$12,000
8	$14,000
9	$17,000
10	$20,000

a) Calculate the Net Present Value (NPV).

b) Instead of forming a partnership with Suzan, Ann has the option to buy a government bond. Ann expects to receive $150 per year for each of the next ten years, and then receive a principle repayment of $50,000. What is the value of a coupon bond that pays $150 per year for each of the next ten years? Assume the rate is 5%.

c) Suppose Ann has the option to buy a new motor home for $25,000 and sell it for $15,000 after six years. Alternatively, she can lease the motor home for $250 per month for six years and return it at the end of the six years. For simplification, assume that lease payments are made yearly instead of monthly and pay at the beginning of each year. If the interest rate, r, is 3.5%, is it better to lease or buy the motor home?

Answer 1

a) Net Present value = sum of present value of cash inflows - initial investment

Sum of Present value of cash inflow = Year 1 cash inflow/(1+discount rate)¹ + Year 2 cash inflow/(1+discount rate)² + Year 3 cash inflow/(1+discount rate)³..... + Year 10 cash inflow/(1+discount rate)¹⁰

NPV = $76,221.41 - $50,000 = $26,221.41

b) We can use financial calculator to find out value of the bond with below key strokes:

N = 10 years; I/Y = interest rate = 5%; PMT = yearly payment = $150; FV = future value = $50,000 > CPT = compute > PV = value of coupon bond = $31,853.92 or $31,854

c) we need to calculate present value of both the options.

Present value of option to buy a home

cost of new home - present value of sale price

cost of new home is already a present value as we have to pay the money now to buy the home. we can sell the house after 6-years. so we need its present value now

$25,000 - $15,000/(1+interest rate)⁶ = $25,000 - $15,000/(1+0.035)⁶ = $25,000 - $15,000/1.035⁶ = $25,000 - $15,000/1.2293 = $25,000 - $12,202 = $12,798

Present value of option to lease home

monthly payment of $250 equals to yearly payment of $250*12 = $3,000.

we need to calculate present value of these six $3,000 yearly payments using financial calculator.

calculator must be in beginning mode.

N = 6 years; I/Y = interest rate = 3.5%; PMT = yearly payment = $3,000; FV = future value = $0 > CPT = compute > PV = present value = $16,545.16

Present value or cost of buying home is $12,798 which is lower than present value of leasing home of $16,545.16. so, it is better to buy the motor home.