Convert the initial investment and annual ZAR cash flows into AED using the given actual spot exchange rates.

Here are the NPV calculations for the project in AED:

c) What is the NPV in AED if the actual pattern of ZAR/AED exchange rates is: S(0) = 3.75; S(1) = 5.7; S(2) = 6.7; S(3) = 7.2; S(4) = 7.7; and S(5) = 8.2?

Step 1: Convert the initial investment and annual ZAR cash flows into AED using the given actual spot exchange rates.
The exchange rate is given as ZAR/AED, meaning 1 AED = X ZAR. To convert ZAR to AED, divide the ZAR amount by the exchange rate.
Initial Investment (Year 0):

$$\text{CF}_0^{\text{AED}} = -\frac{\text{ZAR }10,000,000}{3.75 \text{ ZAR/AED}} = -\text{AED }2,666,666.67$$

Cash Flow Year 1:

$$\text{CF}_1^{\text{AED}} = \frac{\text{ZAR }3,000,000}{5.7 \text{ ZAR/AED}} \approx \text{AED }526,315.79$$

Cash Flow Year 2:

$$\text{CF}_2^{\text{AED}} = \frac{\text{ZAR }4,000,000}{6.7 \text{ ZAR/AED}} \approx \text{AED }597,014.93$$

Cash Flow Year 3:

$$\text{CF}_3^{\text{AED}} = \frac{\text{ZAR }5,000,000}{7.2 \text{ ZAR/AED}} \approx \text{AED }694,444.44$$

Cash Flow Year 4:

$$\text{CF}_4^{\text{AED}} = \frac{\text{ZAR }6,000,000}{7.7 \text{ ZAR/AED}} \approx \text{AED }779,220.78$$

Cash Flow Year 5:

$$\text{CF}_5^{\text{AED}} = \frac{\text{ZAR }7,000,000}{8.2 \text{ ZAR/AED}} \approx \text{AED }853,658.54$$

Step 2: Calculate the present value of each AED cash flow using the parent firm's cost of capital ($k_{AED} = 9.5\% = 0.095$).

$$\text{PV}_t = \frac{\text{CF}_t^{\text{AED}}}{(1 + k_{AED})^t}$$ $$\text{PV}_0 = -\text{AED }2,666,666.67$$ $$\text{PV}_1 = \frac{\text{AED }526,315.79}{(1 + 0.095)^1} = \frac{\text{AED }526,315.79}{1.095} \approx \text{AED }480,653.69$$ $$\text{PV}_2 = \frac{\text{AED }597,014.93}{(1 + 0.095)^2} = \frac{\text{AED }597,014.93}{1.199025} \approx \text{AED }497,917.47$$ $$\text{PV}_3 = \frac{\text{AED }694,444.44}{(1 + 0.095)^3} = \frac{\text{AED }694,444.44}{1.312822375} \approx \text{AED }529,000.00$$ $$$$