DSC1630 Assessment 4 2025 (Accurately Solved) Due 2 October 2025

DSC1630
Assessment 4
Due 2 October 2025

,Question 1 — Present Value of the Cash Outflows
(Sophie)
Problem Statement
Sophie considers purchasing the Ever-so-Young shop. The cash outflows consist of
R500,000 at year 3 and R210,000 at year 9. The borrowing rate is 19% per annum.
Required: determine the present value of the outflows at year 0.


Step 1 — Concept and Formula
The present value (PV) of each outflow is obtained by discounting it back to year 0 at
the borrowing rate:
Ct
P V (Ct ) = , r = 0.19
(1 + r)t

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


Step 3 — Discount Each Outflow
500, 000
P V3 = = 296, 707.91
1.685159
210, 000
P V9 = = 43, 883.03
4.785449

Final Answer
PV of outflows = 296, 707.91 + 43, 883.03 = R340, 590.94




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


Step 1 — Concept and Formula
The future value (FV) of each inflow is compounded to year 9 using:

F V (Ct ) = Ct × (1 + r)9−t , r = 0.175


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


Step 3 — Compound Each Inflow
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


Final Answer
FV of inflows at year 9 = 618, 436.43 + 966, 437.50 + 998, 750.00 = R2, 583, 623.93




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