You're on a roll — Let's calculate the Net Present Value (NPV) for Stellar Trading LLC's project in AED, following the method specified in part (a).
Step 1: Identify the given financial data.
• Initial cost of the project (C0): R10,000,000
• Annual cash flows (CFt) in ZAR:
* Year 1: R3,000,000
* Year 2: R4,000,000
* Year 3: R5,000,000
* Year 4: R6,000,000
* Year 5: R7,000,000
• Parent firm's cost of capital in UAE Dirham (kAED): 9.5% or 0.095
• Long-run inflation in UAE (iAED): 3% or 0.03
• Long-run inflation in South Africa (iZAR): 7% or 0.07
• Current spot foreign exchange rate (ZAR/AED): 3.75
Step 2: Calculate the ZAR equivalent cost of capital (kZAR) using the International Fisher Effect.
The formula for the International Fisher Effect is:
(1+kZAR)=(1+kAED)×(1+iAED)(1+iZAR)
Substitute the given values:
(1+kZAR)=(1+0.095)×(1+0.03)(1+0.07)
(1+kZAR)=1.095×1.031.07
(1+kZAR)=1.095×1.03883495146
(1+kZAR)=1.13752621359
kZAR=1.13752621359−1=0.13752621359
So, the ZAR equivalent cost of capital is approximately 13.75%.
Step 3: Calculate the Net Present Value (NPV) in ZAR.
The NPV formula is:
NPVZAR=−C0+∑t=15(1+kZAR)tCFt
NPVZAR=−10,000,000+(1.13752621359)13,000,000+(1.13752621359)24,000,000+(1.13752621359)35,000,000+(1.13752621359)46,000,000+(1.13752621359)57,000,000
Calculate the present value of each cash flow:
PV(CF1)=1.137526213593,000,000=2,637,300.00
PV(CF2)=(1.13752621359)24,000,000=3,091,360.00
PV(CF3)=(1.13752621359)35,000,000=3,397,050.00
PV(CF4)=(1.13752621359)46,000,000=3,583,620.00
PV(CF5)=(1.13752621359)57,000,000=3,675,490.00
Sum of present values of cash flows = 2,637,300.00+3,091,360.00+3,397,050.00+3,583,620.00+3,675,490.00=16,384,820.00 ZAR
Now, calculate the NPV in ZAR:
NPVZAR=−10,000,000+16,384,820.00=6,384,820.00ZAR
Step 4: Convert the NPV from ZAR to AED at the current spot rate.
The current spot rate is ZAR/AED = 3.75. This means 1 AED = 3.75 ZAR.
NPVAED=SpotRate(ZAR/AED)NPVZAR
NPVAED=3.756,384,820.00
NPVAED=1,702,618.67AED
The NPV for the project in AED, calculated using the ZAR equivalent cost of capital and then converted at the current spot rate, is 1,702,618.67 AED.
NPVAED=1,702,618.67AED
What's next?