(a)

given data:

life of plant = 5 years

tax rate = 50%

method of depriciation = straight line depriciation (non cash expense)

salvage value = zero

cost of plant = 500000

installation cost = 50000

hence, total cost = 500000+50000 = 550000

number of bolltles that can be sold every year = 1000000

cost of one bottle = 1

hence, total revenue every year = 1000000*1 = 1000000

variable cost per bottle = 0.05

total variable cost for 1 million bottles every year = 0.05*1000000 = 50000

fixed cost every year = 200000

hence, total cost every year = total variable cost + fixed cost

= 50000 + 200000

= 250000

REQUIRED: DECISON ON WHETHER WE SHOULD INVEST IN THIS PROJECT OR NOT. THIS CAN BE RE-ITERATED AS WHETHER THE NET PRESENT VALUE(NPV) OF THE PROJECT IS POSITIVE OR NEGATIVE. WE CAN INVEST ONLY IF THE NPV IS POSITIVE.

SOLUTION:

Net NPV is the sum of NPVs of cash flows for five years(project life)

to calculate the NPVs of cash flows for five years, we need to calculate the cash flows every year first which can be calculated as follows:

these are the cash inflows at the end of every year calculated by subtracting the total cost from total revenue and then deduction the tax at rate of 50% from it.

However, there is also a cash outflow made at the start of the first year. i.e. investment cost of 550000

YEAR	NO. OF UNITS	SELLING PRICE OF 1 BOTTLE	TOTLA REVENUE	VAIRABLE COST	FIXED COST	TOTAL COST	PROFIT BEFORE TAX	PROFOT AFTER TAX(50%)
1	1000000	1	1000000	50000	200000	250000	750000	375000
2	1000000	1	1000000	50000	200000	250000	750000	375000
3	1000000	1	1000000	50000	200000	250000	750000	375000
4	1000000	1	1000000	50000	200000	250000	750000	375000
5	1000000	1	1000000	50000	200000	250000	750000	375000

these cash flows needs to be discounted at rate of 10% for 5 years. the discounting factors can be calculated easiy using the NPV formal : DISCOUNTING FACTOR = 1/(1+r)^n, where C is the cash flow, r is the discounting rate and n is the time period. discounting factors for all five years are calculated as follows:

YEAR(n)	r	(1+r)	(1+r)^n	discounting factor 1/(1+r)^n
0	0.1	1.1	1.000	1.000
1	0.1	1.1	1.100	0.909
2	0.1	1.1	1.210	0.826
3	0.1	1.1	1.331	0.751
4	0.1	1.1	1.464	0.683
5	0.1	1.1	1.611	0.621

Calculating the NPVs for individual year cash flows and net NPV:

YEAR	CASH FLOW	DISCOUNTINF FACTOR(AT 10% FOR 5 YEARS)	PRESENT VALUE
0	-550000	1	-550000
1	375000	0.909	340875
2	375000	0.826	309750
3	375000	0.751	281625
4	375000	0.683	256125
5	375000	0.621	232875
		NET NPV	871250

Since, net NPV of the project is POSITIVE, WE SHOUL TAKE ON THIS PROJECT.

(b)

data given:

cost of lodge is K 350 million whic will be paind in five equal installments of K 70 million each at the start of every year. i.e. K 70 million paid now at year = 0

K 130 million spent for imporvement i.e. K 130 million paid now at year = 0

life of project = 5 years

hurdle rate = 15%

annual revenues = K 135 million i.e. cash inflow of K 135 million at the end of every year for next 5 years.

REQUIRED: TO FIND THE NPV OF THE PROJECT

SOLUTION

The discounting factors shall be calculated as mentioned in part (a). the detail of calculation of the same is tabulated as :

YEAR(n)	r	(1+r)	(1+r)^n	1/(1+r)^n
0	0.15	1.15	1.000	1.000
1	0.15	1.15	1.150	0.870
2	0.15	1.15	1.323	0.756
3	0.15	1.15	1.521	0.658
4	0.15	1.15	1.749	0.572
5	0.15	1.15	2.011	0.497

The cash flows are tabulated as follows along with their NPV for respective years and NET NPV :

YEAR	EXPENSES	INCOME	TOTAL CASH INFLOW	DISCOUNTING FACTOR(AT 15% FOR 5 YEARS )	PRESENT VALUE
0	200000000	0	-200000000	1	-200000000
1	70000000	135000000	65000000	0.87	56550000
2	70000000	135000000	65000000	0.756	49140000
3	70000000	135000000	65000000	0.658	42770000
4	70000000	135000000	65000000	0.572	37180000
5	0	135000000	135000000	0.497	67095000
				NPV	52735000

the expenses in year = 0 or at the beginning is K200000000 which is sum of K130 million spent for improvement of lodge and K70 million paid as first installment for purchasing the lodge. Lodge was purchased for 5 equal annual installments of K70 million each which started at year=0 i.e. now and the last installment was paid at the beginning of the 4ht year i.e. year = 4.

Hence, NPV of the cash flows at hurdle rate of 15% is K52735000

Note:

1. all amounts are in currency "K" whether mentioned or not against them.

2. negative cash inflows means expenses/loss for that particular year.