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 machine (A, B, and C), we'll use the given
data and a 12% cost of capital. NPV is calculated by discounting each cash flow to its present
value and then summing them up.
Given:
Cost of capital (discount rate) = 12%
Cash flows:
Machine A:
sql
Copy code
Year 0: -R92,000
Year 1: R12,000
Year 2: R12,000
Year 3: R12,000
Year 4: R12,000
Year 5: R12,000
Machine B:
sql
Copy code
Year 0: -R65,000
, Year 1: R10,000
Year 2: R20,000
Year 3: R30,000
Year 4: R40,000
Year 5: -
Machine C:
sql
Copy code
Year 0: -R100,500
Year 1: R30,000
Year 2: R30,000
Year 3: R30,000
Year 4: R13,000
Year 5: R30,000
To calculate NPV, use the formula: NPV=∑CFt(1+r)t\text{NPV} = \sum \frac{CF_t}{(1 +
r)^t}NPV=∑(1+r)tCFt
Where:
CFtCF_tCFt = Cash flow in period ttt
rrr = Discount rate (12% or 0.12)
ttt = Time period
Let's calculate NPV for each machine:
Machine A:
NPVA=−92,000+12,000(1+0.12)1+12,000(1+0.12)2+12,000(1+0.12)3+12,000(1+0.12)4+12,00
0(1+0.12)5\text{NPV}_A = -92,000 + \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}NPVA=−92,000+(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
Calculating each term:
NPVA=−92,000+12,0001.12+12,0001.2544+12,0001.4049+12,0001.5748+12,0001.7699\
text{NPV}_A = -92,000 + \frac{12,000}{1.12} + \frac{12,000}{1.2544} + \frac{12,000}
{1.4049} + \frac{12,000}{1.5748} + \frac{12,000}{1.7699}NPVA=−92,000+1.1212,000
+1.254412,000+1.404912,000+1.574812,000+1.769912,000
NPVA≈−92,000+10,714.29+9,566.89+8,542.26+7,626.32+6,809.72\text{NPV}_A \approx -
92,000 + 10,714.29 + 9,566.89 + 8,542.26 + 7,626.32 + 6,809.72NPVA
≈−92,000+10,714.29+9,566.89+8,542.26+7,626.32+6,809.72
NPVA≈−92,000+43,259.48\text{NPV}_A \approx -92,000 + 43,259.48NPVA
≈−92,000+43,259.48
NPVA≈−48,740.52\text{NPV}_A \approx -48,740.52NPVA≈−48,740.52
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