Question

A mining company considers opening a new excavation site. The project requires an investment of £25 million at the outset, followed by £17 million in 15 months' time. It is expected that the new site will provide income over a 30 year period starting from the end of the second year. Net income from the project will be received continuously at a rate of £4.7 million per annum. At the end of the 30 years (i.e. 32 years from the start of the project), a final investment of £3 million will be required for environmental regeneration of the site surroundings. Finance is available at an effective rate of interest of 8% per annum. Once the loan is paid off, the company can earn interest on money invested from the venture at an effective rate of interest of 4.5 % per annum. Calculate: The net present value of the project, assuming an effective rate of interest of 8 % per annum (0) 5 marks] The discounted payback period (i) 9 marks] (ii) The accumulated profit at the time the project ends. [4 marks]

Step by step solution needed for all parts of the question and each part with answers thanks ☺

Answer 1

Year 0 investmentment=£25 mn

Investment at the end of 15 month i.e 1.25 years= £17mn, if discounted to present value year 0, value would be =17/(1+8%)^1.25=£15.44mn

Total loan amount at the end of 2nd year= 25*(1.08)^2+17*(1.08)^0.75=£47.17013

Revenue at the end of 2nd year onwards=£4.7 mn per year

If full amount of revenue is repaid in loan, the loan outstanding= 47.17013-4.7=£42.47mn

This loan amount will be repaid in next 16.67 years. Calculation given below:

D E F G -42.47 4.7 PV PMT 8% rate |=NPER( E3,E2,E1) nper NPER(rate, pmt, pv, [fv], [typel)

D E PV -42.47 4.7 PMT 8% rate 16.67537 nper

Now, (2+16.67) or 18.67 years are passed and now revenue of £4.7mn/year will be reinvested @4.5% for next (32-18.67) or 13.33 years

So, value of money will grow at the end of 32 years= £83.36.Calculation given below:

G H J 13.33 nper PMT 4.7 4.50% rate =FV(H3,H1,H2,0) FV FV(rate, nper, pmt, [pv], [typel)

G H 13.33 nper PMT 4.7 4.50% rate ($83.36) FV I

iii) As there is an investment of £3mn at the end of 32 years, so, the accumulated profit at the end of the project = (83.36-3)=£80.36 mn

i) Net present Value of the project= 80.36/(1.08)^32=£6.8466mn

iii) The total discounted expense at year 0= 25+17/(1.08)^1.25+3/(1.08)^32=£40.69mn

Now,

D E F G PV -40.69 nper PMT PMT 4.7 8% rate rate |=NPER(E3,E2,E1) NPER(rate, pmt, pv, [fv], [type]) FV nper LL

E -40.69 PV PMT 4.7 rate 8% 15.32713 nper

So, discounted payback period=15.32 years