Question

Calculate the present value of each of the following cash flows using a discounting rate of 12%
a. $6000 cash inflow at the end of each of the next 6 years.
b. $6000 cash inflow at the beginning of each of the next 6 years.

Answer 1

present value of inflow = cash inflow * present value discounted factor

a. At the end of each year

1^st year =$\dfrac{6000}{1.12}$ =5357.1428

2^ndyear =$\dfrac{6000}{1.12^2}$ =4783.163

^3rd year =$\dfrac{6000}{1.12^3}$ =4270.681

4^thyear =$\dfrac{6000}{1.12^4}$ =3813.108

5^th year =$\dfrac{6000}{1.12^5}$ =3404.561

6^thyear =$\dfrac{6000}{1.12^6}$ =3039.7867

total =$\dfrac{6000}{1.12}+\dfrac{6000}{1.12^2}+\dfrac{6000}{1.12^3}+\dfrac{6000}{1.12^4}+\dfrac{6000}{1.12^5}+\dfrac{6000}{1.12^6}$

=$24668.44

b. At the beginning of each year there will be addition of $6000 at the start

1^st year =6000

2^ndyear =$\dfrac{6000}{1.12^2}$ =4783.163

^3rd year =$\dfrac{6000}{1.12^3}$ =4270.681

4^thyear =$\dfrac{6000}{1.12^4}$ =3813.108

5^th year =$\dfrac{6000}{1.12^5}$ =3404.561

6^thyear =$\dfrac{6000}{1.12^6}$ =3039.7867

$\therefore$ PV =$6000+\dfrac{6000}{1.12^2}+\dfrac{6000}{1.12^3}+\dfrac{6000}{1.12^4}+\dfrac{6000}{1.12^5}+\dfrac{6000}{1.12^6}$

=$25311.30