HOW TO CALCULATE PAYBACK PERIOD & APPROXIMATE RATES OF RETURN. OF A PROJECT

Payback period and approximate rates of return.
Question
Consider the two projects A and B whose cash flows are shown in the table below:
Project A Project B
Init 10 000 15 000
Year Cash inflows
1 3 000 4 200
2 3 000 4 200
3 3 000 4 200
4 3 000 4 200
5 3 000 4200

Determine the payback period (PB) for each project. Include a table containing the necessary payments. (6 marks)
Hint: underline the important terms before attempting to answer a question.

Solution
Formula for payback period
PB= t +  (I-C_t)/(C_(t+1)-C_t )   for c_(t ≤I<C_(t+1) )

Where: C_(t =the cumulative cash flows in years t.)
            I=The initial investment.

YEAR ACCUMULATED CASHFLOWS A ACCUMULATED CASHFLOWS B
1 3 000 4 200
2 6 000 8 400
3 9 000 12 600
4 12 000 16 800
5 15 000 21 000

〖PB〗_(A )=3 +(10 000-9 000)/(12 000 -9 000)
=3 +  1/3
=3.33yrs

〖PB〗_B=3+(15 000-12 600)/(16 800-12 600)
=3+(2 400)/█(4 200@    )
=3.57yrs
Approximate rates of return:
Q: Assuming that the useful life of a project is 10yrs, find the approximates rate of return on the two projects?
Formula is 1/PB
1/〖PB〗_A =1/3.33=30.03%
1/〖PB〗_B =1/3.57=28.01%