4. You’re 20 years old, and you’re trying to decide which career path to take ba

Question

4. You’re 20 years old, and you’re trying to decide which career path to take based on the future expected streams of income. Occupation A has you earning $15,000 for 5 years, then $25,000 for then next 30 years. Occupation B has you earning only $1000 for 4 years, then $10,000 for 6 years, and finally $50,000 for the next 25 years. You plan to retire when you are 55.

a. Write out a formula to calculate the present value of each of these income streams, assuming the interest rate is r. [Hint: you don’t have to write out all 35 terms, you can use “...” when it is obvious what the next term is in a sequence.]

b. What occupation would be better if the interest rate was zero? If it was extremely high?

Explanation / Answer

(a)

(1) PV, Income stream 1 ($)

= 15,000 x PVIFA(r%, 5) + [25,000 x PVIFA(r%, 30) / PVIF(r%, 5)]

(2) PV, income stream 2 ($)

= 1,000 x PVIFA(r%, 4) + [10,000 x PVIFA(r%, 6) / PVIF(r%, 4)] + [50,000 x PVIFA(r%, 25) / PVIF(r%, 10)]

When value of r is know, above can be computed using PVIFA and PVIF tables.

(b) If interest rate is zero, all PVIF values are equal to 1 and all PVIFA values are infinite. PV of the streams cannot be computed.

If interest rate is extremely high, All PVIF values are close to 0, and all PVIFA values are very low. So income stream 1 is better as it gives higher PV.

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