Question

Find the equivalent present value at year 0 of the following cash flows:

1. An annuity with an annual amount of $200, starting from end of year 3 to end of year 8, plus
2. A lump sum cash flow of $1000 at the end of year 6.

Use an annual rate of 8%

Answer 1

Ans A)

Annuity with an annual amount of $200 starting from end of year 3 to end of year 8

Discounting factor for given interest "i" and cash-flow anticipated in year T will be =(1/1+r)^T

We have to multiply future cash-flow with appropriate discount factors that is for cash flow at the end of year 3 will have present value at year 0=200*(1/1.08)^3 and similarly for all other cash flows anticipated

Total sum of all these discounted cash-flows would give present value at year 0

=200*(1/1.08)^3+200*(1/1.08)^4+200*(1/1.08)^5+200*(1/1.08)^6+200*(1/1.08)^7+200*(1/1.08)^8=$792.67

A lump sum cash-flow of $1000 at the end of year 6

=1000*(1/1.08)^6=$630.16

We can add these two cash flows PV to get total Present worth at time 0

Hope this helps best of luck