Capital Budgeting Decision: NPV vs IRR

This article discusses the importance of using NPV method for capital budgeting decisions and compares it with other methods like IRR. It provides a step-by-step calculation of NPV for a given investment and helps in determining whether to proceed with it. The article also explains the concept of WACC and its calculation.

1a) Randolf should use NPV method to make its capital budgeting decision
b) IRR, Payback, Discounted Payback are some other methods which are sometimes used to
make capital budgeting decisions
Randolf should use NPV instead of IRR or any other method because NPV values the exact
amount of profit or loss from the Investment and from the data given it will be possible to
calculate NPV
NPV for Randolf will be : (10 + 10(1.03)/(WACC- 0.03))/WACC – 70
It won't be possible to calculate IRR as the period is perpetuity.
c) To find out if Randolf should go with the investment, we need to find out the NPV
Debt/Equity : 2/3
Thus the weight of debt: 40%
Weight of Equity: 60%
Calculation of Re:
Re = Rf + (rm-rf)B
5.5% + 5.2%*1.2 = 11.74%
Calculation of WACC
Weights Cost Weighted cost
Equity 0.6 11.74% 7.04%
Debt 0.4 6.50% 2.60%
9.64%
Calculation of NPV

Year CF Discount rate PV
0 $ (70.00) 1.0000 $ (70.00)
1 $ 10.00 0.9120 $ 9.12
1 $ 155.03 0.9120 $ 141.39
$ 80.51
Thus NPV: $80.51 Mn
Since NPV is positive, Randolf should go ahead with the investment

2a) WACC is the weighted average cost of capital, it takes into account cost of both equity
and debt, where weights are taken either as market value or book value, whereas expected
return on equity is the return on equity only and not for the company as a whole
We would use WACC to discount, when the project is funded by both debt and equity, for
example, if we are valuing companies and discounting its cashflows, we will use WACC
IF we are valuing a project, which will be funded entirely by equity, then we will use Return
on Equity only.
b)
Value of Debt (Bn)
Enterprise value $ 14.40
Market capitalization $ 10.80
Value of Debt $ 3.60
Cost of Debt:
Kd(1-t)
6.1%(1-35%) 3.97%
Calculation of WACC
Value Weights Cost Weighted cost
Equity $ 10.80 0.75 10.00% 7.50%
Debt $ 3.60 0.25 3.97% 0.99%
$ 14.40 8.49%
WACC: 8.49%
c)

Calculation of NPV
Year CF Discount rate PV
0 $ (100.00) 1.0000 $ (100.00)
1 $ 50.00 0.9217 $ 46.09
2 $ 100.00 0.8496 $ 84.96
3 $ 70.00 0.7831 $ 54.82
$ 85.86
Net present value: $85.86 Bn
No, the risk of this projects FCF is not the same as that of other assets. This project has got its
inherent risk, and other assets have its inherent risks

3a)
Interest rate: the geometric mean of the zero coupon bond rates
7.75%
Price of bond: Present value of coupons + Present value of Face value
Price: $100.99
b)
To make the price of a bond equal to face value, the interest rate shall be equal to the coupon
rate
Since the interest rate is 7.75%, annual coupon rate also equals 7.75%
Annual coupon: 100 x 7.75% = $7.75
c) Price of a bond is dependent on coupon rate and interest rate. If the coupon rate is higher
than the interest rate, the bond trades at a premium, and if the coupon rate is lower than the
interest rate, the bond trades at a discount. In part (a) the coupon rate was 8% whereas the
interest rate was 7.75%. Thus bond was priced more than the face value, and in part (b) the
coupon rate was equal to interest rate, thus price was equal to face value.
d) After the announcement
Price: $ 95.19
Int rate: 9.25%
Annualy compounded return:
9.25% = (6.2%*7.3%*8%*8.6%*x)^(1/5)
X = 22%

The annualy compounded 5 year zero coupon rate for year 5 is 22%
4a) The NPV is
Calculation of NPV
Yea
r CF Discount rate PV
0 -£ 35.00 1.0000 -£ 35.00
1 £ 4.50 0.9259 £ 4.17
2 £ 4.50 0.8573 £ 3.86
3 £ 4.50 0.7938 £ 3.57
4 £ 4.50 0.7350 £ 3.31
5 £ 4.50 0.6806 £ 3.06
6 £ 4.50 0.6302 £ 2.84
7 £ 4.50 0.5835 £ 2.63
8 £ 4.50 0.5403 £ 2.43
9 £ 4.50 0.5002 £ 2.25
10 £ 4.50 0.4632 £ 2.08
-£ 4.80
The NPV is -£4.8 Mn, thus the project shall not be accepted

b)
Calculation of NPV
Yea
r CF Discount rate PV
0 -£ 5.00 1.0000 -£ 5.00
1 £ 3.30 0.9259 £ 3.06
2 £ 3.30 0.8573 £ 2.83
3 £ 3.30 0.7938 £ 2.62
4 £ 3.30 0.7350 £ 2.43
5 £ 3.30 0.6806 £ 2.25
6 £ 3.30 0.6302 £ 2.08
7 £ 3.30 0.5835 £ 1.93
8 £ 3.30 0.5403 £ 1.78
9 £ 3.30 0.5002 £ 1.65
10 -£ 26.70 0.4632 -£ 12.37
£ 3.25
c) No, I do not agree with Mr Murray’s argument. Although the loan total cash flow remains
the same, the timing of cash flow makes the difference. A larger payoff at the end of 10
years, has a very small present value and thereby overvaluing the present value of net cash
flows.
No the NPV calculated by both of them are different, As per Mr Bloomfield, it was a
negative NPV of £4.8 Mn, however as per Mr Murray the NPV is positive £3.25 Mn
Mr Murray has excluded Loan amount and interest payment from cashflows, but he has taken
the cost of the project to calculate the NPV, the cost of the project includes the cost of both

debt and equity, and if the debt is removed, the PV shall be calculated only from the cost of
Equity.
Mr Dick Bloomfield is right in calculating NPV of the project because he includes only the
cash flow from the project and uses Project cost to discount the cash flows.
Since the NPV was ve, MVBC should not go ahead with the project as it is expected to
destroy shareholders wealth.

5a) Since both cost and price are growing at the same rate we can directly calculate the
growth of profit
Gold price $1,500.00 per ounce
cost of extraction $1,200 per ounce
Profit per ounce: $300.00
Present value of Profit: 300*150000*1.04/(10%-4%)
$ 780.00 Mn
NPV: 780 – 500 = 280 Mn
b) Pv of profit at the end of year 11: (150000 x2200 x 1.04)/(0.06) – (150000 x 1776.29
x1.04)/(0.06) = $1101.64Mn
Pv of profit today
150000 Ounces
Year Sale price Cost Price Profit Cash Flows (Mn) Discount factor @ 10%Present value
0 (500.00)$ 1.0000 (500.00)$
1 1,500.00$ 1,200.00$ 300.00$ 45.00$ 0.9091 40.91$
2 $1,560.00 1,248.00$ 312.00$ 46.80$ 0.8264 38.68$
3 $1,622.40 1,297.92$ 324.48$ 48.67$ 0.7513 36.57$
4 $1,687.30 1,349.84$ 337.46$ 50.62$ 0.6830 34.57$
5 $1,754.79 1,403.83$ 350.96$ 52.64$ 0.6209 32.69$
6 $1,824.98 1,459.98$ 365.00$ 54.75$ 0.5645 30.90$
7 $1,897.98 1,518.38$ 379.60$ 56.94$ 0.5132 29.22$
8 $1,973.90 1,579.12$ 394.78$ 59.22$ 0.4665 27.63$
9 $2,052.85 1,642.28$ 410.57$ 61.59$ 0.4241 26.12$
10 $2,134.97 1,707.97$ 426.99$ 64.05$ 0.3855 24.69$
11 $2,200.00 1,776.29$ 423.71$ 63.56$ 0.3505 22.28$
11 1,101.64$ 0.3186 351.02$
195.27$
Per ounce
Calculation of NPV
NPV: 195.27Mn

c) Pv of profit at the end of year 11: (150000 x800 x 1.04)/(0.06) – (150000 x 1776.29
x1.04)/(0.06) = -$2538.36Mn
Pv of profit today
150000 Ounces
Year Sale price Cost Price Profit Cash Flows (Mn) Discount factor @ 10%Present value
0 (500.00)$ 1.0000 (500.00)$
1 1,500.00$ 1,200.00$ 300.00$ 45.00$ 0.9091 40.91$
2 $1,560.00 1,248.00$ 312.00$ 46.80$ 0.8264 38.68$
3 $1,622.40 1,297.92$ 324.48$ 48.67$ 0.7513 36.57$
4 $1,687.30 1,349.84$ 337.46$ 50.62$ 0.6830 34.57$
5 $1,754.79 1,403.83$ 350.96$ 52.64$ 0.6209 32.69$
6 $1,824.98 1,459.98$ 365.00$ 54.75$ 0.5645 30.90$
7 $1,897.98 1,518.38$ 379.60$ 56.94$ 0.5132 29.22$
8 $1,973.90 1,579.12$ 394.78$ 59.22$ 0.4665 27.63$
9 $2,052.85 1,642.28$ 410.57$ 61.59$ 0.4241 26.12$
10 $2,134.97 1,707.97$ 426.99$ 64.05$ 0.3855 24.69$
11 $800.00 1,776.29$ (976.29)$ (146.44)$ 0.3505 (51.33)$
11 (2,538.36)$ 0.3186 (808.80)$
(1,038.15)$
Per ounce
Calculation of NPV
There will be a negative NPV of $1038.15 Mn
d) Only in B2, the company should close the mine in Year 10, because if the mine is
continued there will be a negative NPV in B2
And if the mine is stopped in B1, there is a negative NPV of $178.02 Mn
150000 Ounces
Year Sale price Cost Price Profit Cash Flows (Mn) Discount factor @ 10%Present value
0 (500.00)$ 1.0000 (500.00)$
1 1,500.00$ 1,200.00$ 300.00$ 45.00$ 0.9091 40.91$
2 $1,560.00 1,248.00$ 312.00$ 46.80$ 0.8264 38.68$
3 $1,622.40 1,297.92$ 324.48$ 48.67$ 0.7513 36.57$
4 $1,687.30 1,349.84$ 337.46$ 50.62$ 0.6830 34.57$
5 $1,754.79 1,403.83$ 350.96$ 52.64$ 0.6209 32.69$
6 $1,824.98 1,459.98$ 365.00$ 54.75$ 0.5645 30.90$
7 $1,897.98 1,518.38$ 379.60$ 56.94$ 0.5132 29.22$
8 $1,973.90 1,579.12$ 394.78$ 59.22$ 0.4665 27.63$
9 $2,052.85 1,642.28$ 410.57$ 61.59$ 0.4241 26.12$
10 $2,134.97 1,707.97$ 426.99$ 64.05$ 0.3855 24.69$
(178.02)$
Calculation of NPV
Per ounce

e) If the probability is 50%,
NPV :
150000 Ounces
Year Sale price Cost Price Profit Cash Flows (Mn) Discount factor @ 10%Present value
0 (500.00)$ 1.0000 (500.00)$
1 1,500.00$ 1,200.00$ 300.00$ 45.00$ 0.9091 40.91$
2 $1,560.00 1,248.00$ 312.00$ 46.80$ 0.8264 38.68$
3 $1,622.40 1,297.92$ 324.48$ 48.67$ 0.7513 36.57$
4 $1,687.30 1,349.84$ 337.46$ 50.62$ 0.6830 34.57$
5 $1,754.79 1,403.83$ 350.96$ 52.64$ 0.6209 32.69$
6 $1,824.98 1,459.98$ 365.00$ 54.75$ 0.5645 30.90$
7 $1,897.98 1,518.38$ 379.60$ 56.94$ 0.5132 29.22$
8 $1,973.90 1,579.12$ 394.78$ 59.22$ 0.4665 27.63$
9 $2,052.85 1,642.28$ 410.57$ 61.59$ 0.4241 26.12$
10 $2,134.97 1,707.97$ 426.99$ 64.05$ 0.3855 24.69$
11 $1,500.00 1,776.29$ (276.29)$ (41.44)$ 0.3505 (14.53)$
11 (718.36)$ 0.3186 (228.89)$
(421.44)$
Calculation of NPV
Per ounce
If the mine is closed in 10 years:
150000 Ounces
Year Sale price Cost Price Profit Cash Flows (Mn) Discount factor @ 10%Present value
0 (500.00)$ 1.0000 (500.00)$
1 1,500.00$ 1,200.00$ 300.00$ 45.00$ 0.9091 40.91$
2 $1,560.00 1,248.00$ 312.00$ 46.80$ 0.8264 38.68$
3 $1,622.40 1,297.92$ 324.48$ 48.67$ 0.7513 36.57$
4 $1,687.30 1,349.84$ 337.46$ 50.62$ 0.6830 34.57$
5 $1,754.79 1,403.83$ 350.96$ 52.64$ 0.6209 32.69$
6 $1,824.98 1,459.98$ 365.00$ 54.75$ 0.5645 30.90$
7 $1,897.98 1,518.38$ 379.60$ 56.94$ 0.5132 29.22$
8 $1,973.90 1,579.12$ 394.78$ 59.22$ 0.4665 27.63$
9 $2,052.85 1,642.28$ 410.57$ 61.59$ 0.4241 26.12$
10 $2,134.97 1,707.97$ 426.99$ 64.05$ 0.3855 24.69$
(178.02)$
Calculation of NPV
Per ounce
Value to the company to close the mine:
421.44 – 178.02 = $243.42 Mn