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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Birdie

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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.

A) A single payment of $75,000 received in 5 years:

To calculate the present value, we use the formula:

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:

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:

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:

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:

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:

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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