Ann and Suzan are classmates who graduated with business degrees from Athabasca

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%.

a) Does the partnership offer a rate of return in excess of 4%? Make sure to show the calculation of the new rate of return.

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 four years and return it at the end of the four years. For simplification, assume that lease payments are made yearly instead of monthly.

i) If the interest rate, r, is 3.5%, is it better to lease or buy the motor home?

ii) At what interest rate would you be indifferent between buying and leasing the motor home?

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

Explanation / Answer

Ann would be indifferent between lease and buy option at interest rate of 1.77%

a) Year Cashflows Dicounting Factor @ 4% Present Value 0 -50000 1 -50000 1 2000                                         0.96                   1,923 2 4000                                         0.92                   3,698 3 6000                                         0.89                   5,334 4 7000                                         0.85                   5,984 5 8000                                         0.82                   6,575 6 10000                                         0.79                   7,903 7 12000                                         0.76                   9,119 8 14000                                         0.73                 10,230 9 17000                                         0.70                 11,944 10 20000                                         0.68                 13,511 NPV                 26,221 Discounting Factor is calculated as (1/(1+r)^-n)

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