Question

You have invested in a diamond mine in Nigeria. The mine is expected to generate nominal, after-tax cash flow of $1 million per year in perpetuity at a risk-adjusted discount rate of 12.5% per year. Unfortunately, the Nigerian government requires that you leave each year's Cash flow in the Nigerian Treasury for five years after it is earned. The discount rate on the five-year Nigerian bonds is 10%. Assume end of year cash flows

a. What is the value of the diamond mine in the absence of blocked funds

b. What is the loss in value if blocked funds earn 0% interest

c. What is the loss in value if blocked funds earn 5% interest

d. What is the loss in value if blocked funds earn 10% interest

Answer 1

	After tax Cash flow = $ 1 Million per year
	Risk Adjusted discount Rate = 12.5%
	Life of mine = Perpetual
a.	Value of Diamond Mine = PV of Future expected cash flows
	Value of Diamond Mine = PV of Cash flows per year / Discount Rate
	Value of Diamond Mine = $ 1 Million / 12.5%
	Value of Diamond Mine = $ 1,000,000 / 12.5%
	Value of Diamond Mine = $ 8,000,000 = $ 8 Million
	If the Nigerian government requires to leave each year's Cash flow in the Nigerian Treasury for five years after it is earned
b.	If blocked funds earn 0% interest
	Value of Diamond Mine = PV of Future expected cash flows
	PV of Expected Cash flows per annum = [$ 1 Million*FV(0%, 5 yrs)] / PV(12.5%,5 years)
	PV of Expected Cash flows per annum = [$ 1 Million * (1+0)^5] / (1+0.125)^5
	PV of Expected Cash flows per annum = ($ 1 Million * 1) / 0.5549
	PV of Expected Cash flows per annum = $ 1 Million * 0.5549
	PV of Expected Cash flows per annum = $ 554,928.96
	Value of Diamond Mine = PV of Future expected cash flows
	Value of Diamond Mine = PV of Cash flows per year / Discount Rate
	Value of Diamond Mine = $ 554,928.96 / 12.5%
	Value of Diamond Mine = $ 4,439,431.66
	Loss in Value on account of restriction = $ 8 Million - $ 4,439,431.66
	Loss in Value on account of restriction = $ 3,560,568.34
c.	If blocked funds earn 5% interest
	Value of Diamond Mine = PV of Future expected cash flows
	PV of Expected Cash flows per annum = [$ 1 Million*FV(5%, 5 yrs)] / PV(12.5%,5 years)
	PV of Expected Cash flows per annum = [$ 1 Million * (1+0.05)^5] / (1+0.125)^5
	PV of Expected Cash flows per annum = ($ 1 Million * 1.276) / 0.5549
	PV of Expected Cash flows per annum = $ 1,276,000 * 0.5549
	PV of Expected Cash flows per annum = $ 708,052.40
	Value of Diamond Mine = PV of Future expected cash flows
	Value of Diamond Mine = PV of Cash flows per year / Discount Rate
	Value of Diamond Mine = $ 708,052.40 / 12.5%
	Value of Diamond Mine = $ 5,664,419.20
	Loss in Value on account of restriction = $ 8 Million - $ 5,664,419.20
	Loss in Value on account of restriction = $ 2,335,580.80
d.	If blocked funds earn 10% interest
	Value of Diamond Mine = PV of Future expected cash flows
	PV of Expected Cash flows per annum = [$ 1 Million*FV(10%, 5 yrs)] / PV(12.5%,5 years)
	PV of Expected Cash flows per annum = [$ 1 Million * (1+0.1)^5] / (1+0.125)^5
	PV of Expected Cash flows per annum = ($ 1 Million * 1.6110) / 0.5549
	PV of Expected Cash flows per annum = $ 1,611,000 * 0.5549
	PV of Expected Cash flows per annum = $ 893,943.90
	Value of Diamond Mine = PV of Future expected cash flows
	Value of Diamond Mine = PV of Cash flows per year / Discount Rate
	Value of Diamond Mine = $ 893,943.90 / 12.5%
	Value of Diamond Mine = $ 7,151,551.20
	Loss in Value on account of restriction = $ 8 Million - $ 7,151,551.20
	Loss in Value on account of restriction = $ 848,448.80