Question

You are offered to invest in a project with the following cash flow profile. What is the future worth (i.e., at t = 10) of this investment to you if your MARR is 7%?

t	0	1	2	3	4	5	6	7	8	9	10
$ in million	-10	0	0	0	0	5	5	5	5	5	7.5

A. $20.1 million

B. $18.6 million

C. $16.1 million

D. $14.6 million

My answer is B but I just want to double check if it is.

Answer 1

B $18.6 million This is the CORRECT answer

Detailed working as follows :-

P_i = Cash Flow in Year i

r = 7% = 0.07

A_i = Future value in year 10 of year i Cash flow

A_i = P_i * (1 + r)^(10-i) ; where i is from 0 to 9

P₀ = -10

A₀ = -10 * (1 + 0.07)¹⁰ = -10 * (1.07)¹⁰ = -10 * 1.967 = -19.67

P₁ = 0

A₁ = 0 * (1 + 0.07)⁹ = 0 * (1.07)⁹ = 0 * 1.838 = 0

P₂ = 0

A₂ = 0 * (1 + 0.07)⁸ = 0 * (1.07)⁸ = 0 * 1.718 = 0

P₃ = 0

A₃ = 0 * (1 + 0.07)⁷ = 0 * (1.07)⁷ = 0 * 1.606 = 0

P₄ = 0

A₄ = 0 * (1 + 0.07)⁶ = 0 * (1.07)⁶ = 0 * 1.501 = 0

P₅ = 5

A₅ = 5 * (1 + 0.07)⁵ = 5 * (1.07)⁵ = 5 * 1.403 = 7.01

P₆ = 5

A₆ = 5 * (1 + 0.07)⁴ = 5 * (1.07)⁴ = 5 * 1.311 = 6.55

P₇ = 5

A₇ = 5 * (1 + 0.07)³ = 5 * (1.07)³ = 5 * 1.225 = 6.13

P₈ = 5

A₈ = 5 * (1 + 0.07)² = 5 * (1.07)² = 5 * 1.145 = 5.72

P₉ = 5

A₉ = 5 * (1 + 0.07)¹ = 5 * (1.07)¹ = 5 * 1.07 = 5.35

P₁₀ = 7.5

A₁₀ = 7.5

Future Worth FW = Σ A_i    ; where i is from 0 to 10

                            = -19.6 + 0 + 0 + 0 + 0 + 7.01 + 6.55 + 6.13 +5.72 + 5.35 + 7.5

                            = 18.6 (rounded)

Future worth of Revenue at year 10 is $18.6 million