DSC1630 Assessment 4 2025 (Accurate Solutions) Due 2 October 2025

DSC1630
Assessment 4
Due 2 October 2025

,Question 1 — Present Value of Cash Outflows
(Sophie)
Problem Statement
Sophie faces cash flows with outflows of R500,000 at year 3 and R210,000 at year 9.
The borrowing rate is 19% per annum. Required: compute the present value (PV) of
these outflows at year 0.


Step 1 — Formula
Ct
P V (Ct ) = , r = 0.19
(1 + r)t

Step 2 — Discount Factors
1.193 = 1.685159, 1.199 = 4.785449


Step 3 — Compute Present Values
500, 000
P V3 = = 296, 707.91
1.685159
210, 000
P V9 = = 43, 883.03
4.785449

Step 4 — Total Present Value
P Voutflows = 296, 707.91 + 43, 883.03 = 340, 590.94


Final Answer
Present Value of Outflows ≈ R340, 590.94




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, Question 8 — Future Value of Cash Inflows (Sophie)
Problem Statement
Cash inflows: R200,000 at year 2, R700,000 at year 7, and R850,000 at year 8. The
reinvestment rate is 17.5% per annum. Required: compute the future value (FV) of
these inflows at year 9.


Step 1 — Formula
F V (Ct ) = Ct (1 + g)9−t , g = 0.175


Step 2 — Growth Factors
1.1757 = 3.092182, 1.1752 = 1.380625, 1.1751 = 1.175


Step 3 — Compute Future Values
F V200 = 200, 000 × 3.092182 = 618, 436.43

F V700 = 700, 000 × 1.380625 = 966, 437.50

F V850 = 850, 000 × 1.175 = 998, 750.00


Step 4 — Total Future Value
F Vinflows at year 9 = 618, 436.43 + 966, 437.50 + 998, 750.00 = 2, 583, 623.93


Final Answer
Future Value of Inflows at t = 9 ≈ R2, 583, 623.93




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