Question

Calculate the equivalent series of annual payments (where the payments are made at the end of the year in each of periods 1 to 4) for an investment with a capital cost of $1,500 and annual cash flows as shown in the table below. The salvage value of the investment at the end of Year 4 is $1,200 The interest rate, compounded annually, is 16%. Please be careful about the signs. Costs have negative signs but income and Salvage Value have positive signs. This is why the capital cost C is a negative number in the table. C-$1,500$600-$500I-$400I-$300 L-$1,200 4 C: Cost, I: Income, L: Salvage Value

Answer 1

Answer

equivalent series of annual payments

discounted cash flow = cash flow * pv factor

c = -1500 * 1

= - 1500

1 st year = 600 * 1 / 1 + 0.16

= 600 * 0.8621

= 517.24

2 nd year = 500 * 1 / ( 1 + 0.16 )²

= 500 * 0.7432

= 371.58

3 rd year = 400 * 1 / (1 + 0.16 )³

= 400 * 0.6407

= 256.26

4 th year = 300 * 1 / ( 1 + 0.16 )⁴

= 300 * 0.5523

= 165.69

salvage value = 1200 * 1 / ( 1+ 0.16 )⁴

= 1200 * 0.5523

= 662.75

net present value = -1500 + 517.24+371.58+256.26+165.69+662.75

= 473.52

present value for future annual cash flow

= ( 1 + p.i.r )ⁿ - 1 / (p.i.r ) * ( 1 + p.i.r )ⁿ

= ( 1 + 0.16 ) ⁴ - 1 / 0.16 * ( 1 + 0.16 )⁴

= 1.811 - 1 / 0.16 * 1.811

= 2.798

present value of saving = payment per period * present value of interest rate factor

473.52 = payment per period * 2.798

payment per period = 473.52 / 2.798

equivalent series of annual payment = 169.24