Question

Assume a two-period world, perfect certainty, and perfect capital market. A firm has an initial endowment of $75 million. The firm has identified the following available investment opportunities:

Proposal	Period-0 Outlay	Period-1 Return
K	$9.77 million	$10.63 million
L	$10.82 million	$13.21 million
M	$13.63 million	$15.81 million
N	$12.12 million	$14.25 million
R	$19.26 million	$21.76 million

These are not divisible projects, which cannot be invested in a fraction (the firm must invest 100 percent of each proposal or none of it). Assume that the average market rate of return is 12.8 percent.
(i) Which projects will the firm undertake to maximise the value of the firm?
(ii) If the firm undertakes projects that will maximise the value of the firm, how much money will it invest in period-0 (now)?
(iii) Does the firm need borrowing in period-0? If yes, how much? Why?
(iv) What period-0 dividend will be paid to shareholders (owners)?
(v) What will the period-1 (next) dividend be?
(vi) What is the Present Value (PV) of period-1 returns from optimum investment in (ii)?
(vii) What is the Net Present Value (NPV) from optimum investment in (ii)?
(viii) How will the value of the firm change due to the decision of optimum investment in (ii)?
(ix) How would your answers from (i) to (viii) above change if the firm had an initial endowment of $20 million only?

Answer 1

i) Rate of Return from a project = (Period 1 return - Period 0 outlay)/ period 0 Outlay

 

Example : Rate of Return from Project K = ($10.63 million - $9.77 million) / $9.77 million = 8.802%

Similarly , Rate of return of all projects are calculated ,

If the rate of return is more than market rate of return of 12.8% , the project is accepted , otherwise rejected.

 

The complete calculations are shown below

Proposal	Period 0 Outlay (million $)	Period 1 Return (million $)	Rate of return	Accepted
K	9.77	10.63	8.802%	No
L	10.82	13.21	22.089%	Yes
M	13.63	15.81	15.994%	Yes
N	12.12	14.25	17.574%	Yes
R	19.26	21.76	12.980%	Yes

 

So, the firm will undertake Proposal L, M, N and R to maximise the value of the firm

 

ii) Total amount invested in period 0 (now)

=Total Amount of period 0 outlay of proposals undertaken

= $(10.82+13.63+12.12+19.26) million

= $55.83 million

 

iii) As the amount required for investment is less than the endowment amount of $75 million, the firm does not need any borrowing

 

iv) Period 0 dividend paid to owners

= Endowment amount - Total amount invested

=$75 milllion - $55.83 million

= $19.17 million

 

v) Period 1 dividend will be the Return amount of the proposals undertaken

= $(13.21+15.81+14.25+21.76) million

= $65.03 million

 

vi) Present value of period 1 returns from Optimum investment

= $65.03 million / 1.128

= $57.65071 million

 

vii) NPV from optimum investment

= Present value of period 1 returns - amount invested in period 0

=$57.65071 million - $55.83 million

= $1.820709 million

 

viii) The value of the firm will increase by the NPV value i.e. the value of the firm will increase by $1.820709 million due to the decision of optimum investment in (ii)

 

ix) If the firm had an endowment of only $20 million, the firm will still undertake Proposal L, M, N and R to maximise the value of the firm

Total amount invested in period 0 (now)

=Total Amount of period 0 outlay of proposals undertaken

= $(10.82+13.63+12.12+19.26) million

= $55.83 million

 

As the amount required for investment is more than the endowment amount of $75 million, the firm will need to borrow $55.83 million - $20 million = $35.83 million

 

Period 0 dividend paid to owners

= 0 (as the firm does not have any excess cash and is borrowing)

Period 1 dividend will be the Return amount of the proposals undertaken less future value of amount borrowed

= $(13.21+15.81+14.25+21.76) million - $35.83 million * 1.128

= $24.61376 million

 

Present value of period 1 returns from Optimum investment

= $24.61376 million / 1.128

= $21.82071 million

 

NPV from optimum investment

= Present value of period 1 returns - own amount invested in period 0

=$21.82071 million - $20 million

= $1.820709 million

 

The value of the firm will increase by the NPV value i.e. the value of the firm will increase by $1.820709 million due to the decision of optimum investment in (ii)

i) So, the firm will undertake Proposal L, M, N and R to maximise the value of the firm