Question

Private cars is a medium size car manufacturer planning to start a new business of sports cars.

As part of Initial investment, the firm needs to purchase manufacturing equipment worth $ 10 million today and also incur an additional R&D cost of $ 2 million.

The equipment will be depreciated in equal amounts over the next 10 years.

In the first year, the firm expects to sell 100 cars at $ 25,000 each and the manufacturing cost is estimated to be $ 15,000 per car.

As demand rises and processes are streamlined, the firm expects revenues to grow by 7% each year for the first 10 years and remain constant from the 11^thyear onwards into the indefinite future

Over the same period, cost of manufacturing is expected to rise by only 2% per year and stabilize from the 11^thyear onwards.

Note: The project doesn’t terminate in 10 years but continues into the indefinite future

To guard against contingencies, the firm needs to set aside $ 3 million at the start of the project. However, as the project develops, the contingency amount can be reduced by              $ 300,000 each year.

From the 11^thyear onwards, the firm does not envisage buying or selling off any additional equipment or incurring any costs beyond the cost of manufacturing the cars.

To fund the project the firm borrows $ 5 million from the bank which charges an interest rate of 4%. The loan will need to be repaid in equal-sized annual instalments over 10 years, starting in Year 1.

The rest of the funding comes from shareholders who expect an 8% return on their investment.

The corporate tax rate is 40% and expected to remain constant.

Calculate the NPV of the project.

Answer 1

WACC calculation
Year 0 cash flows
Initial investment	-10000000
R&D costs	-2000000
Contingency fund	-3000000
Total funding reqd.	-15000000
Funded From :		Propn.	Cost	Prop.*Cost
Bank Loan	5000000	33.33%	0.024	0.80%
Equity	10000000	66.67%	0.08	5.33%
Total	15000000		WACC=	6.13%

To fund the project the firm borrows $ 5 million from the bank which charges an interest rate of 4%. The loan will need to be repaid in equal-sized annual instalments over 10 years, starting in Year 1.

The equal annual pmts. Will be

5000000=Pmt.*(1-1.04^-10)/0.04

Solving the above,

the annuity will be $ 616455

We can know the annual interest payment from the amortisation table (below)

Year	Annuity	Tow. Int.at 4% *Prev.Loan bal.	Tow. Loan(Annuity-Int.)	Loan bal.	Int.tax shield(Int.*40%)
0				5000000
1	616455	200000	416455	4583545	80000
2	616455	183342	433113	4150432	73337
3	616455	166017	450438	3699994	66407
4	616455	148000	468455	3231539	59200
5	616455	129262	487193	2744345	51705
6	616455	109774	506681	2237664	43910
7	616455	89507	526948	1710716	35803
8	616455	68429	548026	1162689	27371
9	616455	46508	569947	592742	18603
10	616455	23710	592745	-3	9484
Total	6164550	1164547	5000003		465819

NPV Analysis                /     Year	0	1	2	3	4	5	6	7	8	9	10
1.Initial investment	-10000000
2.R&D costs	-2000000
3.Contingency fund	-3000000	300000	300000	300000	300000	300000	300000	300000	300000	300000	300000
Opg. Cash flows:
4.Sales revenue(g=7%)		2500000	2675000	2862250	3062608	3276990	3506379	3751826	4014454	4295465	4596148
5.Terminal value of sales(4596148/0.0613)											74977945
6.Total sales revenues(4+5)		2500000	2675000	2862250	3062608	3276990	3506379	3751826	4014454	4295465	79574093
7. Mfg. costs(g=2%)		1500000	1530000	1560600	1591812	1623648	1656121	1689244	1723029	1757489	1792639
8.Terminal value of costs(1792639/0.0613)											29243703
9. Total mfg.costs(7+8)		1500000	1530000	1560600	1591812	1623648	1656121	1689244	1723029	1757489	31036342
10.EBT(6-9)		1000000	1145000	1301650	1470796	1653342	1850258	2062582	2291425	2537976	48537751
11. Tax at40%(10*40%)		400000	458000	520660	588318	661337	740103	825033	916570	1015191	19415100
12. EAT(10-11)		600000	687000	780990	882477	992005	1110155	1237549	1374855	1522786	29122650
13. Depn. Tax shields(10000000/10*40%)		400000	400000	400000	400000	400000	400000	400000	400000	400000	400000
14.Interest tax shields(as in Amortsn. Sch.)		80000	73337	66407	59200	51705	43910	35803	27371	18603	9484
15. Net annual cash flows(1+2+3+12+13+14)	-15000000	1380000	1460337	1547397	1641677	1743710	1854064	1973352	2102227	2241389	29832134
16.PV f at 6.13%(1/1.0613^Yr.n)	1	0.94224	0.88782	0.83654	0.78822	0.74269	0.69980	0.65938	0.62129	0.58541	0.55159
17.PV at 6.31%(15*16)	-15000000	1300292	1296512	1294456	1294002	1295041	1297466	1301180	1306093	1312121	16455182
18. NPV (Sum of Row 17)	13152344

Year	0	1	2	3	4	5	6	7	8	9	10
Contingency fund reqd.	-3000000	-2700000	-2400000	-2100000	-1800000	-1500000	-1200000	-900000	-600000	-300000	0
Change in the fund(Yr.1-Yr.0)&so on		300000	300000	300000	300000	300000	300000	300000	300000	300000	300000