What is the valuation using WACC of 11% and FCF of $400,00 with constant growth

Question

What is the valuation using WACC of 11% and FCF of $400,00 with constant growth of 5%?

a. 7770000 b. 6000000 c. 7000000 d. 6666667

2. A friend has asked your financial advice. He would like to have $2,500,000 in his investment account 25 years from now. He expects a stable 6% return and has $500,000 now.

a How much does he need to add to his account annually to achieve his goal?

b What would he need to add annually if his return was reduced to 5.5%?

c What would he need to add annually if his return was increased to 7%?

Explanation / Answer

Solution:

1. WACC (K) = 11%, FCF = $400,000, g = 5%
Valuation = FCF * (1+g)/(K-g)
                = 400,000 * (1+5%)/(11%-5%)
                = 420,000/6%
                = 7,000,000
Hence option C is the answer

2. Future value = $2,500,000 , Time (t) = 25 years, Return (r) = 6%
He has $500,000 currently which can be invested at a rate of 6% for 25 years,
After 25 years, 500,000 would be equal to 500,000 (1+6%)25
                     = 500,000 * 4.292
                     = 2,145,935.4
Thus, he would be having $2,145,935.4 with him after 25 years, he would still require
                   2,500,000 - 2,145,935.4 = $354,064.6
Part a. He requires $354,064.6 after 25 years. Let x be the amount he needs to save annually at 6%
              Applying the formula for annuity payments
       FV = P * [((1+i)25 - 1)/i]
354,064.6 = P * [((1+6%)25 - 1)/6%]
   354,064.6 = P * (3.292/6%)
Hence, P = 354,064.6*6%/3.292
                  = 354,064.4/54.86
                  = 6,453.44
Hence, he needs to save $6,453.4 annually to achieve his goal of $2,500,000 after 25 years

Part b. When r = 5.5%,
After 25 years, 500,000 would be equal to 500,000 (1+5.5%)25
                     = 500,000 * 3.813
                     = 1,906,696.2
Thus, he would be having $1,906,696.2 with him after 25 years, he would still require
                   2,500,000 - 1,906,696.2 = $593,303.8
By again using annuity formula,

P = (593,303.8*5.5%)/[(1+5.5%)25 - 1]
    = 32,631.71/2.813
    = 11,598.71
Hence, he needs to save $11,598.7 annually to achieve his goal of $2,500,000 after 25 years

C. When r = 7%,
After 25 years, 500,000 would be equal to 500,000 (1+7%)25
                     = 500,000 * 5.427
                     = 2,713,716.3
Thus, he would be having $2,713,716.3 with him after 25 years, which is more than the required amount by
                   2,500,000 - 2,713,716.3 = -$213,716.3
hence, he does not need to save any amount in this case

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