Question

cise 4 GBP, 000 e oject GBP A British multinational anticipates cash flows of 100 min GBP, 120 mln GBP and 160 min inves If the en ussia. three first 06 year respe e 00 return on the inve t is 17 per cent, how large does the probability of expropriation in yond. erpetu ears OP he pect nbau probal erms? Btne nent befor the i invest NPV have Assum that reaks ment элә even qual t nba e Boe hne the e w in y vent riation 360 exprop ea r 5 in Бхә

Answer 1

The present value is 660 million GBP with 0% probability of expropriation.

Formula for present value = cash flow divided by (1+ rate of return) to the power time in years

Present value formula for perpetuity is = cash flow divided by (rate of return)

Year	Cash flow	Present Value	formulae
0	(790)	(790)	790/(1+17%)^0
1	100	85	100/(1+17%)^1
2	120	88	120/(1+17%)^2
3	160	100	160/(1+17%)^3
4	200	1,176	200/(17%)
		660	sum total

	164		1,176	(517)
Probability of expropriation	present value of consideration	probability of perpetual cash flow	present value of perpetuity	present value (year 0-3)	Net present value
0%	-	100%	1176	(517)	660
10%	16	90%	1059	(517)	558
20%	33	80%	941	(517)	457
30%	49	70%	824	(517)	356
40%	66	60%	706	(517)	255
50%	82	50%	588	(517)	153
60%	99	40%	471	(517)	52
70%	115	30%	353	(517)	(49)
80%	131	20%	235	(517)	(150)
90%	148	10%	118	(517)	(252)
100%	164	0%	0	(517)	(353)

Explanation:-

• If the probability of expropriation is 0%, then we will continue to receive 200 mn GBP in perpetuity from year 4 onwards (amount = 200/17% = 1176 mn GBP). Hence, the total present value = present value from year 0-3 + present value of perpetuity + present value of expropriation consideration (which is 0) = -517+1176+0 = 660 mn GBP
• If the probability of expropriation is 10%, then there is a 10% chance that in year 5 we will receive 360 and we will not receive 200 in perpetuity. Present value of this consideration is 360/(1+17%)^5 = 164 mn GBP. And there is a 90% chance that we will receive 200 in perpetuity. Hence the net present value = -517+1176*90%+164*10%= 558mn GBP
• ..and so on
• As per the table we see that at probability of expropriation of 60%, the net present value is almost equal to zero, i.e. investment breaks even in NPV.

Hence, answer = 60%