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FIN3701 Assignment 1 (COMPLETE ANSWERS) Semester 2 2024 (232195) - DUE 20 August 2024
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- FIN3701
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- 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, you'll need to discount the annual
cash inflows back to their present value using the firm's cost of capital, which is 12%. The NPV
formula is:
NPV=∑Ct(1+r)t−I0\text{NPV} = \sum \frac{C_t}{(1 + r)^t} - I_0NPV=∑(1+r)tCt−I0
where:
CtC_tCt = cash inflow in year ttt
rrr = discount rate (12% or 0.12)
ttt = year
I0I_0I0 = initial investment
Let's calculate the NPV for each machine.
Machine A
Initial Investment: −R92,000-R92,000−R92,000
Annual Cash Inflows: R12,000 for 6 years
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
Let's calculate each term:
1. 12,000(1+0.12)1=12,0001.12=10,714.29\frac{12{,}000}{(1 + 0.12)^1} = \
frac{12{,}000}{1.12} = 10{,}714.29(1+0.12)112,000=1.1212,000=10,714.29
2. 12,000(1+0.12)2=12,0001.2544=9,550.13\frac{12{,}000}{(1 + 0.12)^2} = \
frac{12{,}000}{1.2544} = 9{,}550.13(1+0.12)212,000=1.254412,000=9,550.13
3. 12,000(1+0.12)3=12,0001.4049=8,550.53\frac{12{,}000}{(1 + 0.12)^3} = \
frac{12{,}000}{1.4049} = 8{,}550.53(1+0.12)312,000=1.404912,000=8,550.53
4. 12,000(1+0.12)4=12,0001.5735=7,627.19\frac{12{,}000}{(1 + 0.12)^4} = \
frac{12{,}000}{1.5735} = 7{,}627.19(1+0.12)412,000=1.573512,000=7,627.19
5. 12,000(1+0.12)5=12,0001.7623=6,812.46\frac{12{,}000}{(1 + 0.12)^5} = \
frac{12{,}000}{1.7623} = 6{,}812.46(1+0.12)512,000=1.762312,000=6,812.46
6. 12,000(1+0.12)6=12,0001.9738=6,086.22\frac{12{,}000}{(1 + 0.12)^6} = \
frac{12{,}000}{1.9738} = 6{,}086.22(1+0.12)612,000=1.973812,000=6,086.22
Adding these present values:
10,714.29+9,550.13+8,550.53+7,627.19+6,812.46+6,086.22=49,340.8210{,}714.29 +
9{,}550.13 + 8{,}550.53 + 7{,}627.19 + 6{,}812.46 + 6{,}086.22 =
49{,}340.8210,714.29+9,550.13+8,550.53+7,627.19+6,812.46+6,086.22=49,340.82
Now subtract the initial investment:
NPVA=49,340.82−92,000=−42,659.18\text{NPV}_A = 49{,}340.82 - 92{,}000 = -
42{,}659.18NPVA=49,340.82−92,000=−42,659.18
Machine B
Initial Investment: −R65,000-R65,000−R65,000
Annual Cash Inflows for years 1 to 5: R10,000, R20,000, R30,000, R40,000 (no inflow for year
6)
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+30,000(1+0.12)
5−65,000\text{NPV}_B = \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} + \frac{30{,}000}{(1 +
0.12)^5} - 65{,}000NPVB=(1+0.12)110,000+(1+0.12)220,000+(1+0.12)330,000
+(1+0.12)440,000+(1+0.12)530,000−65,000
Let's calculate each term:
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