Your colleague has asked you to consider and investment of $250,000 to her KLW c

Question

Your colleague has asked you to consider and investment of $250,000 to her KLW compact fitness equipment business that will build and sell compact fitness equipment specialized for small apartments and condos in Vancouver. These items would fold and fit into bookcases and wall doors. Funds would be used to complete the prototype, obtain patents and set up manufacturing Terms of the proposal are that you would receive $50,000 at the end of each year in interest with the full $250,000 to be repaid at the end of a tenyear period. a. Assuming a 10% required rate of return, calculate the present value of cash flows and the net present value of the proposed investment. b. Based on this same interest rate assumption, calculate the cumulative cash flow of the proposed investment for each period in both nominal (without and discount rate – just add the cash flows) and present value terms. c. What is the payback period in both nominal and presentvalue terms? d. Can the presentvalue payback period ever be shorter than the nominal payback period?

Explanation / Answer

a. The present value of the cash flow is given by =pv(rate,nper,pmt,fv) formula in excel where

rate = 10% = 0.10, nper= 10 year =10, pmt = 50000 and FV =250000

The present value of the investment =pv(0.10,10,50000,250000) = $403,614.18

The present value of the investment =  $403,614.18

b. The nominal cumlautive cash flows are as shown in the table below:

The cumulative cash flows with discount rate is as shown below:

c. Payback period in nomial value terms is 5 years - as cumulative cash flows is 0 in year 5

Payback period in present value terms = 7 + 6579.06/23325.37 = 7 + 0.28 = 7.28 years

d. Yes present value payback period can be shorter than nominal payback period if the discount rate is negative.

Year Cash flows Cumulative cash flows 0 -250000 -250000 1 50000 -200000 2 50000 -150000 3 50000 -100000 4 50000 -50000 5 50000 0 6 50000 50000 7 50000 100000 8 50000 150000 9 50000 200000 10 300000 500000

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