FIN3701 Assignment 1 (Semester 2, 2025).
QUESTION 1 — Replacement decision (8)
Data (from the question): old machine cost R1,000,000, depreciated at 30% reducing
balance for 3 years; can be sold now for R900,000. New machine cost R700,000 +
installation R20,000 + transport R5,000; working capital decreases by R8,000. Assume
40% capital gains tax.
1.1 Book value of the existing machine (2)
Reducing-balance book value after 3 years at 30% p.a.:
BV_3 = 1,000,000 × (1 − 0.30)^3 = 1,000,000 × 0.7^3 = R343,000
Answer: R343,000
1.2 Tax implication on sale (2)
Sale proceeds now: R900,000
Book value: R343,000
Capital gain = 900,000 − 343,000 = R557,000
Capital gains tax (given) = 40% × 557,000 = R222,800
Answer: Tax payable = R222,800
1.3 After-tax proceeds from sale (2)
After-tax proceeds = Sale price − CGT = 900,000 − 222,800 = R677,200
Answer: R677,200
1.4 Initial investment for the replacement (2)
Formula: Initial outlay = Cost of new + install + transport + ΔNWC − after-tax
proceeds(old)
, Here ΔNWC = −R8,000 (a decrease releases cash).
= 700,000 + 20,000 + 5,000 − 8,000 − 677,200 = R39,800
Answer: R39,800
QUESTION 2 — Choose between Projects X and Y (12)
Firm’s cost of capital = 11%. Cash flows are as given in the question:
Project X: invest 400,000; inflows (years 1–4) = 140,000; 165,000; 190,000; 190,000.
Project Y: invest 525,000; inflows (years 1–6) = 175,000; 150,000; 125,000; 100,000;
80,000; 50,000.
NPV at 11%
NPV_X = −400,000
140,000/1.11 + 165,000/1.11² + 190,000/1.11³ + 190,000/1.11⁴ = +R124,129 (≈
124,129.08)
NPV_Y = −525,000
175,000/1.11 + 150,000/1.11² + 125,000/1.11³ + 100,000/1.11⁴ + 80,000/1.11⁵ +
50,000/1.11⁶ = −R14,119 (≈ −14,118.81)
IRR (for completeness)
IRR_X ≈ 24.03%
IRR_Y ≈ 9.85%
Decision (considering risk concepts)
For mutually exclusive projects, choose the project with the higher NPV at the firm’s
required return. Project X has a strong positive NPV and IRR well above 11%; Project Y
destroys value at 11% (negative NPV) and its IRR is below the hurdle.
QUESTION 1 — Replacement decision (8)
Data (from the question): old machine cost R1,000,000, depreciated at 30% reducing
balance for 3 years; can be sold now for R900,000. New machine cost R700,000 +
installation R20,000 + transport R5,000; working capital decreases by R8,000. Assume
40% capital gains tax.
1.1 Book value of the existing machine (2)
Reducing-balance book value after 3 years at 30% p.a.:
BV_3 = 1,000,000 × (1 − 0.30)^3 = 1,000,000 × 0.7^3 = R343,000
Answer: R343,000
1.2 Tax implication on sale (2)
Sale proceeds now: R900,000
Book value: R343,000
Capital gain = 900,000 − 343,000 = R557,000
Capital gains tax (given) = 40% × 557,000 = R222,800
Answer: Tax payable = R222,800
1.3 After-tax proceeds from sale (2)
After-tax proceeds = Sale price − CGT = 900,000 − 222,800 = R677,200
Answer: R677,200
1.4 Initial investment for the replacement (2)
Formula: Initial outlay = Cost of new + install + transport + ΔNWC − after-tax
proceeds(old)
, Here ΔNWC = −R8,000 (a decrease releases cash).
= 700,000 + 20,000 + 5,000 − 8,000 − 677,200 = R39,800
Answer: R39,800
QUESTION 2 — Choose between Projects X and Y (12)
Firm’s cost of capital = 11%. Cash flows are as given in the question:
Project X: invest 400,000; inflows (years 1–4) = 140,000; 165,000; 190,000; 190,000.
Project Y: invest 525,000; inflows (years 1–6) = 175,000; 150,000; 125,000; 100,000;
80,000; 50,000.
NPV at 11%
NPV_X = −400,000
140,000/1.11 + 165,000/1.11² + 190,000/1.11³ + 190,000/1.11⁴ = +R124,129 (≈
124,129.08)
NPV_Y = −525,000
175,000/1.11 + 150,000/1.11² + 125,000/1.11³ + 100,000/1.11⁴ + 80,000/1.11⁵ +
50,000/1.11⁶ = −R14,119 (≈ −14,118.81)
IRR (for completeness)
IRR_X ≈ 24.03%
IRR_Y ≈ 9.85%
Decision (considering risk concepts)
For mutually exclusive projects, choose the project with the higher NPV at the firm’s
required return. Project X has a strong positive NPV and IRR well above 11%; Project Y
destroys value at 11% (negative NPV) and its IRR is below the hurdle.
