Tutorial paper

SCHOOL OF FINANCE AND APPLIED STATISTICS
FINANCIAL MATHEMATICS
(STAT 2032 / STAT 6046)
TUTORIAL SOLUTIONS WEEK 8
Question 1
This question refers to two projects relating to a small software company that has asked to set up a new computer system for a major client. :
Project A
Project A delegates all the development work to outside companies. The estimated cashflows for Project A are (where brackets indicate expenditure):
Beginning of year 1
Beginning of year 2
Beginning of year 3
End of year 3

contractors’ fees contractors’ fees contractors’ fees sales ($150,000)
($250,000)
($250,000)
$1,000,000

Project B
Project B carries out all the development work in-house by purchasing the necessary equipment and using the company’s own staff. The estimated cashflows for Project B are:
Beginning of year 1
Throughout year 1
Throughout year 2
Throughout year 3
End of year 3

new equipment staff costs staff costs staff costs sales ($325,000)
($75,000)
($90,000)
($120,000)
$1,000,000

The staff costs can be assumed to be paid uniformly throughout the year.
(a) Calculate the net present value for Project A and Project B using a risk discount rate of 10% per annum. Using net present value as a criterion, which project is preferable? (b) Find the internal rates of return for Project A and Project B, and hence determine which project is more favourable using this criterion.

1

Solution
(a)
For Project A, the net present value (in $000) is:
NPVA (0.10) = −150 − 250v − 250v 2 + 1000v3 = 167.4
For Project B, the net present value (in $000) is:

NPVB (0.10) = −325 − 75a1 − 90va1 − 120v 2 a1 + 1000v3
= −325 − (75 + 90v + 120v 2 )

1− v

δ

+ 1000v3 = 182.1

So, using a risk discount rate of 10%, Project B appears more favourable.

(b)
For Project A, we need to find the interest rate i that satisfies the equation of value:
−150 − 250v − 250v 2 + 1000v 3 = 0
At 10%: −150 − 250v − 250v 2 + 1000v3 = 167.4
At 20%: