Answer to Question #179189 in Financial Math for Bishem

Question

1. Project A requires an initial outlay of K2 000 but will return K4 000 at the end of 

each of years 2, 3 and 4 whereas project B requires an initial outlay of K1 400 but 

will return K3 500 at the end of years 1, 2, 3 and 4.

(i) Calculate the NPV of each project if the discount rate is 5% compounded 

annually. On the basis of this, which project would you invest in?

(ii) Estimate the IRR for each of these projects. On the basis of the IRR which 

project would you prefer?

2. A project requiring an initial outlay of K15 000 is guaranteed to produce a return of 

K20000 in three years` time. Use the

(a) net present value

(b) internal rate of return

To decide whether this is worthwhile if the capital could be invested 

elsewhere at 15 % compounded annually.

Answer 1

(1)

(I)$PV=\frac {FV}{(1+r)^{n}}$

PV=present value

FV=future value

r=interest rate in decimal

n=number of years

2nd year PV$=\frac{4000}{1.05^{2}}=3628.117914$

3rd year PV$=\frac{4000}{1.05^{3}}=3455.350394$

4rth year PV$=\frac{4000}{1.05^{4}}=3290.809899$

PV$=3628.117914 +3455.350394+3290.809899=10374.27785$

NPV$=10374.27785-2000=8374.2777853$

2nd year PV$=\frac{3500}{1.05}=3333.333333$

2nd year PV$=\frac{3500}{1.05^{2}}=3174.603175$

3rd year PV$=\frac{3500}{1.05^{3}}=3023.431595$

4th year PV$=\frac{3500}{1.05^{4}}=2879.458662$

PV$=3333.333333+3333+3174.603175+3023.431595+2879.458662=12410.82676$

NPV$=12410.82676-1400=1010.82676$

project B

(II)$0=NPV=\frac {Cn}{(1+r)^{n}}$

Cn=cash flow

n=total number of periods

r=internal rate of return

$-2000+\frac{3628.12}{(1+r)^{2}}+\frac{3455.35}{(1+r)^{3}}+\frac{3290.81}{(1+r)^{4}}=80.888$ %

$-14000+\frac{3333.33}{(1+r)}+\frac{3174.60}{(1+r)^{2}}+\frac{3023.43}{(1+r)^{3}}+\frac{2875.46}{(1+r)^{4}}=231.715$ %

Project A

(2)

(a)1st year PV$=\frac{20000}{1.15}=17391.30430$

2nd year PV$=\frac{20000}{1.15^{2}}=15122.87335$

3rd year PV$=\frac{20000}{1.15^{3}}=13150.3245$

PV$=17391.30430+15122.87335+13150.3245=45664.5022$

NPV$=45664.5022-15000=30664.5022$

the project is worthwhile

(b)

$-1500+\frac{17391.30}{(1+r)}+\frac{15122.87}{(1+r)^{2}}+\frac{13150}{(1+r)^{3}}=92.154$ %

the project is worthwhile