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Calculate the Net Present Value (NPV) in AED for Stellar Trading LLC's project, given initial cost, annual cash flows in ZAR, parent firm's cost of capital in AED, inflation rates in UAE and South Afr

Business/Management

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Answer

NPVAED=1,702,618.67 AEDNPV_{AED} = 1,702,618.67 \text{ AED}

Step-by-step solution

4 steps

Let's calculate the Net Present Value (NPV) for Stellar Trading LLC's project in AED, following the method specified in part (a).

  1. Identify the given financial data.

    • Initial cost of the project (C0C_0): R10,000,000
    • Annual cash flows (CFtCF_t) 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 (kAEDk_{AED}): 9.5% or 0.095
    • Long-run inflation in UAE (iAEDi_{AED}): 3% or 0.03
    • Long-run inflation in South Africa (iZARi_{ZAR}): 7% or 0.07
    • Current spot foreign exchange rate (ZAR/AED): 3.75

  2. Calculate the ZAR equivalent cost of capital (kZARk_{ZAR}) using the International Fisher Effect.

    The formula for the International Fisher Effect is:

    (1+kZAR)=(1+kAED)×(1+iZAR)(1+iAED)(1 + k_{ZAR}) = (1 + k_{AED}) \times \frac{(1 + i_{ZAR})}{(1 + i_{AED})}

    Substitute the given values:

    (1+kZAR)=(1+0.095)×(1+0.07)(1+0.03)(1 + k_{ZAR}) = (1 + 0.095) \times \frac{(1 + 0.07)}{(1 + 0.03)} (1+kZAR)=1.095×1.071.03(1 + k_{ZAR}) = 1.095 \times \frac{1.07}{1.03} (1+kZAR)=1.095×1.03883495146(1 + k_{ZAR}) = 1.095 \times 1.03883495146 (1+kZAR)=1.13752621359(1 + k_{ZAR}) = 1.13752621359 kZAR=1.13752621359−1=0.13752621359k_{ZAR} = 1.13752621359 - 1 = 0.13752621359

    So, the ZAR equivalent cost of capital is approximately 13.75%.

  3. Calculate the Net Present Value (NPV) in ZAR.

    The NPV formula is:

    NPVZAR=−C0+∑t=15CFt(1+kZAR)tNPV_{ZAR} = -C_0 + \sum_{t=1}^{5} \frac{CF_t}{(1 + k_{ZAR})^t} NPVZAR=−10,000,000+3,000,000(1.13752621359)1+4,000,000(1.13752621359)2+5,000,000(1.13752621359)3+6,000,000(1.13752621359)4+7,000,000(1.13752621359)5NPV_{ZAR} = -10,000,000 + \frac{3,000,000}{(1.13752621359)^1} + \frac{4,000,000}{(1.13752621359)^2} + \frac{5,000,000}{(1.13752621359)^3} + \frac{6,000,000}{(1.13752621359)^4} + \frac{7,000,000}{(1.13752621359)^5}

    Calculate the present value of each cash flow:

    PV(CF1)=3,000,0001.13752621359=2,637,300.00PV(CF_1) = \frac{3,000,000}{1.13752621359} = 2,637,300.00 PV(CF2)=4,000,000(1.13752621359)2=3,091,360.00PV(CF_2) = \frac{4,000,000}{(1.13752621359)^2} = 3,091,360.00 PV(CF3)=5,000,000(1.13752621359)3=3,397,050.00PV(CF_3) = \frac{5,000,000}{(1.13752621359)^3} = 3,397,050.00 PV(CF4)=6,000,000(1.13752621359)4=3,583,620.00PV(CF_4) = \frac{6,000,000}{(1.13752621359)^4} = 3,583,620.00 PV(CF5)=7,000,000(1.13752621359)5=3,675,490.00PV(CF_5) = \frac{7,000,000}{(1.13752621359)^5} = 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=16,384,820.002,637,300.00 + 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=6,384,820.00 ZARNPV_{ZAR} = -10,000,000 + 16,384,820.00 = 6,384,820.00 \text{ ZAR}

  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=NPVZARSpot Rate (ZAR/AED)NPV_{AED} = \frac{NPV_{ZAR}}{\text{Spot Rate (ZAR/AED)}} NPVAED=6,384,820.003.75NPV_{AED} = \frac{6,384,820.00}{3.75} NPVAED=1,702,618.67 AEDNPV_{AED} = 1,702,618.67 \text{ AED}

    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.

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