Exam (elaborations)
FIN3701 Assignment 1 (COMPLETE ANSWERS) Semester 2 2024 (232195) - DUE 20 August 2024
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- FIN3701
- Institution
- University Of South Africa
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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 of the three machines, we need to discount
the future cash inflows to the present value using the firm's cost of capital, which is 12%. The
NPV is the sum of these discounted cash inflows minus the initial investment.
The formula for NPV is:
NPV=∑(Ct(1+r)t)−C0\text{NPV} = \sum \left( \frac{C_t}{(1 + r)^t} \right) -
C_0NPV=∑((1+r)tCt)−C0
where:
CtC_tCt = cash inflow at time ttt
rrr = discount rate (cost of capital)
ttt = time period
C0C_0C0 = initial investment
Let's calculate the NPV for each machine.
Machine A
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 = \left( \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} \right) - 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
Machine B
NPVB=(10,000(1+0.12)1+20,000(1+0.12)2+30,000(1+0.12)3+40,000(1+0.12)4)−65,000\
text{NPV}_B = \left( \frac{10,000}{(1 + 0.12)^1} + \frac{20,000}{(1 + 0.12)^2} + \
frac{30,000}{(1 + 0.12)^3} + \frac{40,000}{(1 + 0.12)^4} \right) - 65,000NPVB
=((1+0.12)110,000+(1+0.12)220,000+(1+0.12)330,000+(1+0.12)440,000)−65,000
Machine C
NPVC=(30,000(1+0.12)1+30,000(1+0.12)2+30,000(1+0.12)3+13,000(1+0.12)4+30,000(1+0.12)
5)−100,500\text{NPV}_C = \left( \frac{30,000}{(1 + 0.12)^1} + \frac{30,000}{(1 + 0.12)^2}
+ \frac{30,000}{(1 + 0.12)^3} + \frac{13,000}{(1 + 0.12)^4} + \frac{30,000}{(1 + 0.12)^5} \
right) - 100,500NPVC=((1+0.12)130,000+(1+0.12)230,000+(1+0.12)330,000+(1+0.12)413,000
+(1+0.12)530,000)−100,500
Now, let's calculate these NPVs step by step.
Calculation
First, we need to compute the present value of each cash inflow. I'll use Python to ensure
accuracy.
Python Calculation
Let's calculate these values in Python.
The NPVs for each of the machines are as follows:
Machine A: NPV = −R42,663.11- R42,663.11−R42,663.11
Machine B: NPV = R6,646.58R6,646.58R6,646.58
Machine C: NPV = −R3,160.52- R3,160.52−R3,160.52
Based on these calculations, Machine B has the highest NPV and is the most favorable
investment among the three options.
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