FIN3701 Assignment 1 (COMPLETE ANSWERS) Semester 2 2024 (232195) - DUE 20 August 2024

FIN3701 Assignment 1
(COMPLETE ANSWERS)
Semester 2 2024 (232195) - DUE
20 August 2024
100% GUARANTEED

,FIN3701 Assignment 1 (COMPLETE ANSWERS)
Semester 2 2024 (232195) - DUE 20 August 2024
QUESTION 1 [20 marks] Batlokwa Industries wishes to
select one of three possible machines, each of which is
expected to satisfy the firm’s ongoing need for additional
aluminium extrusion capacity. The three machines, A, B
and C, are equally risky. The firm plans to use a 12% cost
of capital to evaluate each of them. The initial investment
and annual cash inflows over the life of each machine are
shown in the following table: Year Machine A Machine B
Machine C 0 (R92 000) (R65 000) (R100 500) 1 R12 000
R10 000 R30 000 2 R12 000 R20 000 R30 000 3 R12 000
R30 000 R30 000 4 R12 000 R40 000 R13 000 5 R12 000
- R30 000 6 R12 000 - REQUIRED: 1.1 Calculate the NPV
for each of the three projects. (9 marks)
To calculate the Net Present Value (NPV) for each machine, we need to discount the future cash
inflows to their present values using the cost of capital, and then subtract the initial investment.

Here are the steps to calculate the NPV:

1. List the cash flows: Identify the initial investment and the annual cash inflows for each
machine.
2. Discount the cash flows: Use the formula to find the present value of each cash flow.
3. Calculate the NPV: Subtract the initial investment from the sum of the present values of
the cash inflows.

The formula for calculating the present value (PV) of a future cash flow is:

PV=C(1+r)tPV = \frac{C}{(1 + r)^t}PV=(1+r)tC

where:

 CCC = Cash flow in year ttt
 rrr = Discount rate (cost of capital)
 ttt = Year

The formula for NPV is:

, NPV=∑t=1nCt(1+r)t−Initial InvestmentNPV = \sum_{t=1}^n \frac{C_t}{(1 + r)^t} - \
text{Initial Investment}NPV=∑t=1n(1+r)tCt−Initial Investment

where:

 CtC_tCt = Cash flow at year ttt
 rrr = Discount rate
 nnn = Number of years

Let's perform the calculations for each machine.

Machine A

 Initial Investment: −R92,000-R92,000−R92,000
 Cash Flows:
o Year 1: R12,000
o Year 2: R12,000
o Year 3: R12,000
o Year 4: R12,000
o Year 5: R12,000
o Year 6: R12,000

NPV Calculation:

NPVA=12,000(1+0.12)1+12,000(1+0.12)2+12,000(1+0.12)3+12,000(1+0.12)4+12,000(1+0.12)
5+12,000(1+0.12)6−92,000\text{NPV}_A = \frac{12{,}000}{(1 + 0.12)^1} + \frac{12{,}000}
{(1 + 0.12)^2} + \frac{12{,}000}{(1 + 0.12)^3} + \frac{12{,}000}{(1 + 0.12)^4} + \
frac{12{,}000}{(1 + 0.12)^5} + \frac{12{,}000}{(1 + 0.12)^6} - 92{,}000NPVA
=(1+0.12)112,000+(1+0.12)212,000+(1+0.12)312,000+(1+0.12)412,000+(1+0.12)512,000
+(1+0.12)612,000−92,000
NPVA=12,0001.12+12,0001.2544+12,0001.4049+12,0001.5735+12,0001.7623+12,0001.9715−
92,000\text{NPV}_A = \frac{12{,}000}{1.12} + \frac{12{,}000}{1.2544} + \frac{12{,}000}
{1.4049} + \frac{12{,}000}{1.5735} + \frac{12{,}000}{1.7623} + \frac{12{,}000}{1.9715} -
92{,}000NPVA=1.1212,000+1.254412,000+1.404912,000+1.573512,000+1.762312,000
+1.971512,000−92,000
NPVA=10,714.29+9,576.62+8,564.50+7,629.46+6,800.41+5,981.95−92,000\text{NPV}_A =
10{,}714.29 + 9{,}576.62 + 8{,}564.50 + 7{,}629.46 + 6{,}800.41 + 5{,}981.95 -
92{,}000NPVA=10,714.29+9,576.62+8,564.50+7,629.46+6,800.41+5,981.95−92,000
NPVA=48,666.23−92,000\text{NPV}_A = 48{,}666.23 - 92{,}000NPVA=48,666.23−92,000
NPVA=−43,333.77\text{NPV}_A = -43{,}333.77NPVA=−43,333.77

Machine B

 Initial Investment: −R65,000-R65,000−R65,000
 Cash Flows:
o Year 1: R10,000