Question 4 Billy and Bob are both 50 years old and work at the same rm. Billy is

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Question 4 Billy and Bob are both 50 years old and work at the same rm. Billy is a more able individual and presently earns $90,000/year; Bob earns $50,000/year. They have the opportunity to enroll in a job-training course for a one-time cost of $10,000. The raise to which they are entitled depends on how much they learn in the course. Again, since Billy is more able, he expects to earn an additional $2,000/year, while Bob expects to earn only an additional $1,000/year. Both workers have a discount rate of 5%.

a. If both workers expect to work until age 60 (i.e., ten more years), will either opt to take the course?

b. What is the minimum number of years each worker needs to work before retiring if the course is to be a wise investment?

Explanation / Answer

(a) The workers will take up the course if present value (PV) of additional annual income equals the current cost of the course.

For Billy:

PV = $2,000 x PVIFA(5%, 10 years) = $2,000 x 7.7217 (From PVIFA table) = $15,443

Since Billy can recover the course costs from future discounted cash flows, he will opt.

For Bob:

PV = $1,000 x PVIFA(5%, 10 years) = $1,000 x 7.7217 (From PVIFA table) = $7,721.7

Since Bob cannot recover the course costs from future discounted cash flows, he will not opt.

(b) We computed the discounted payback period (DPBP), which is the time by when future discounted cash flows recover the course cost, i.e. year by when cumulative discounted cash flows are zero.

Billy has a DBPB between 5 & 6 years, so he must work for minimum 5 years to recover the cost.

Bob cannot recover the cost within 10 years (until retirement).

(a) Billy Year Cash flow Discount factor @5% Discounted cash flow Cumulative discounted cash flow 0 -10,000 1.0000 -10,000 -10,000 1 2,000 0.9524 1,905 -8,095 2 2,000 0.9070 1,814 -6,281 3 2,000 0.8638 1,728 -4,554 4 2,000 0.8227 1,645 -2,908 5 2,000 0.7835 1,567 -1,341 6 2,000 0.7462 1,492 151

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