Question

You have done a great job, and your boss offers you a few different possible gifts. Using a discount rate of 10%, which present would you choose? A) A single payment of $75,000 received in 5 years B) $8,000 per year for 10 years, starting two year from now C) One payment of $47,500 received today D) A growing perpetuity that pays $2000 each year starting one year from now. The perpetuity grows at a rate of 1.5% per year. E) All the presents stated are equally good!

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Answer to a math question You have done a great job, and your boss offers you a few different possible gifts. Using a discount rate of 10%, which present would you choose? A) A single payment of $75,000 received in 5 years B) $8,000 per year for 10 years, starting two year from now C) One payment of $47,500 received today D) A growing perpetuity that pays $2000 each year starting one year from now. The perpetuity grows at a rate of 1.5% per year. E) All the presents stated are equally good!

Expert avatar
Birdie
4.5
36 Answers
To determine which present is the best option, we need to calculate the present value of each option using a discount rate of 10%.

A) A single payment of $75,000 received in 5 years:
To calculate the present value, we use the formula:
PV = \frac{FV}{(1 + r)^n}
Where PV is the present value, FV is the future value, r is the discount rate, and n is the number of years.
Plugging in the values, we have:
PV_A = \frac{75000}{(1 + 0.10)^5} = \$49707.65

B) $8,000 per year for 10 years, starting two years from now:
To calculate the present value of an annuity, we use the formula:
PV = C \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)
Where PV is the present value, C is the annual cash flow, r is the discount rate, and n is the number of years.
Using the values given, we have:
PV_B = 8000 \times \left(\frac{1 - (1 + 0.10)^{-10}}{0.10}\right) = \$60247.36

C) One payment of $47,500 received today:
Since this is the present value, the value remains the same.

D) A growing perpetuity that pays $2000 each year starting one year from now, growing at a rate of 1.5% per year:
The present value of a growing perpetuity can be calculated using the formula:
PV = \frac{C}{{r - g}}
Where PV is the present value, C is the annual cash flow, r is the discount rate, and g is the growth rate.
Plugging in the values, we have:
PV_D = \frac{2000}{{0.10 - 0.015}} = \$22222.22

Therefore, the present value of each option is:
A) \$49,707.65
B) \$60,247.36
C) \$47,500.00
D) \$22,222.22

Since option B has the highest present value, I would choose option B, which is receiving $8,000 per year for 10 years, starting two years from now.

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