Question

Giant Equipment Ltd. is considering two projects to invest next year. Both projects have the same start-up costs. Project A will produce annual cash flows of $42,000 at the beginning of each year for eight years. Project B will produce cash flows of $48,000 at the end of each year for seven years. The company requires a 12% return.
Required:
b Which project should the company select if the interest rate is 14% at the cash flows in Project Bis also at the beginning of each year? (5 marks)

Answer 1

Answer:

the company should invest in Project A to earn 12% return!

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Answer 2

Project "A" is more feasible

Explanation:

a) We must calculate the Present Value  of both the project to understand which project the company must select

Project A

Annual Cash flows  (CF) = $ 42000

Rate of return (r)= 12%

no. of years (n) =8

Present value of annuity P = CF x ((1 – (1 / (1 + r) ^ -n)) / r)

= $42000 ((1- (1 /1+0.12) ^ -8)/ 0.12)

= $ 233677.77

Project B

Annual Cash flows  (CF) = $ 48000

Rate of return (r)= 12%

no. of years (n) =7

Present value of annuity P = CF x ((1 – (1 / (1 + r) ^ -n)) / r)

= 48000 ((1- (1 /1+0.12) ^ -7)/ 0.12)

= $ 219060.31

The company must opt for project A since project A gives more cash flow when compared to project B

b) when the interest rate is 14 per cent r) and cash flows in Project B is also at the beginning of each year, using the above formula we will get

Project A = $ 222108.80

Project B =  $ 234656.04

Thus , in this case Project B must be opted since, project B gives more cash flows

Present Value of Annuity

• The annuity's present value is the monetary equivalent of all the "future annuity payments". A part of the equation is the rate of return (r) or discount rate. Future payments in an annuity are decreased according to the discount rate. So the higher the interest rate, the "lower" the "annuity's present value".  An "annuity 's present value" is dependent on the sum of money in time. One can invest money so as to make "more money" via interest and other mechanisms of return.

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