Question

o The initial capital cost will be $500,000 paid at the beginning of year 1 (i.e., immediately). The impact on cottage owners will involve a loss of $50,000 at the end of each year for the first four years (because of the construction activities affecting property values) but cottage owners will benefit by $55,000 per year in perpetuity from the end of year 5 onwards. The benefits from recreational fishing will not start until the end of year 5 and will be $35,000 per year in perpetuity. Development, stocking and management costs of the recreational fishery will start at the beginning of year 3 and continue forever. These costs are $10,000 per year

0. The province is considering a water resource development that will enhance recreational fishing and recreational cottage values (property values).

   1. a) Calculate the net present value using a 5% discount rate. Interpret the result. (15 points)

   2. b) Calculate the gross benefit cost ratio using a discount rate of 5%. Interpret the result. (5 points)

   3. c) Which value best approximates the internal rate of return: 4 %, 5%, 6%, 7%, 8%, or 9%? (Note – you are not being asked to calculate the internal rate of return!) (5 points)

Answer 1

a)

Calculation of Net present value at 5 % discount Rate.

NPV= Present Value of Cash inflows - Present value of Cash outflows

Given,

initial capital cost =$ 500000

Loss for first four Years= 50000

Perpetual costs from 3 rd year begening is= $10000 per year

Perpetual costs in current value at 5% rate= 10000/5%= $ 200000

So, calculation of PV of Cash out flows

Outflows	year	PV factor/ PV annuity factor at 5%	value	PV out flows
initial capital cost will	0	1	500000	500000
Loss for first four Years	1 to 4	3.545950504	50,000	177297.5252
perpetual cost		0.907029478	200000	181405.8957
PV of cash outflows				858703.4209

Given,

Perpetual benefit from end of 5 th yearis=55000 per year

Perpetual benefit at current value at 5 % rate= 55000/5%=$ 1100000

Perpetual benefit from end of 5 th yearis=35000 per year

Perpetual benefit at current valueat 5 % rate= 35000/5%=$ 700000.

inflows	year	PV factor/ PV annuity factor at 5%	value	PV in flows
Perpetual benfit from 5th year end		0.783526166	1100000	861878.8
Recreational Perpetual benfit from 6 th year end		0.783526166	700000	548468.3
PV of cash inflows				1410347

                 

NPV=1410347-858703=$ 55643.

b)

gross benefit cost ratio using a discount rate of 5% is=

PV ofcash inflows/PV of cash out flows=1410347/858703= 1.64

c)

At IRR, PV ofcash inflows= PV of cash out flows

So calculation of IRR

At 8%,PV of cash inflows=

inflows	year	PV factor/ PV annuity factor at 5%	value	PV in flows
Perpetual benfit from 5th year end		0.680583197	687500	467900.9
Recreational Perpetual benfit from 6 th year end		0.680583197	437500	297755.1
PV of cash inflows				765656.1

PV of Cash out flows

Outflows	year	PV factor/ PV annuity factor at 5%	value	PV out flows
initial capital cost will	0	1	500000	500000
Loss for first four Years	1 to 4	3.312126840	50,000	165606.342
perpetual cost		0.85733882	125000	107167.3525
PV of cash outflows				772773.6945

So, At 8% PV of cash in flows = PV of cash out flows

IRR is 8%.