Question

9. Wyoming Natural Gas, Inc. is weighing a drilling venture into the Teton Mountains. The venture re- quires an initial outlay of $73M, but is anticipated to generate a perpetual series of $10M cash flows starting one year from today. 12.5% is the appropriate required rate of return for valuing this venture. a. Calculate the project's NPV. b. Now, suppose that the perpetual series of cash flows starts at t=5 instead of at t=1. Recalculate NPV.

Answer 1

(a) NPV is the present value of future Cash flows

NPV =  ΣCFn/(1+r)n, where CFn is the cash Flow in year n, r = rate of return = 12.5%

Given,

CF0 = $ - 73 m

CF1, CF2, ..... = $10m

Hence, NPV = -CF0 + CF1/(1+r) + CF2/(1+r)² + ......

= -73 + 10/(1+0.125) + 10/(1+0.125)² + .....

= -73 + 10/0.125

= $7 m

(b)

Given,

CF0 = $ - 73 m

CF5, CF6, ..... = $10m

Hence, NPV = -CF0 + CF5/(1+r)⁵ + CF6/(1+r)⁶ + ...... = -CF0 + 1/(1+r)⁴ [ CF5/(1+r)⁵ + CF6/(1+r)⁶ + ...... ]

= -73 + 1/(1+0.125)⁴[ 10/(1+0.125) + 10/(1+0.125)² + ..... ]

= -73 + [1/(1+0.125)⁴][10/0.125]

= $ -23.05 m