Question

Suppose your production opportunity set in a world of perfect certainty consists of the following possibilities:

Project	Investment Outlay	Rate of Return %
A	$1,000,000	8
B	1,000,000	20
C	2,000,000	4
D	3,000,000	30

a) Graph the production opportunity set in a C0, C1 framework.

b) If the market rate of return is 10%, draw in the capital market line for the optimal investment decision.

Suppose your production opportunity set in a world of perfect certainty consists of the following possibilities: Project Investment Outlay Rate of Return (%) A $1,000,000 8 B 1,000,000 20 2,000,000 D 3,000,000 30 (a) Graph the production opportunity set in a concı framework. (b) If the market rate of return is 10%,draw in the capital market line for the optimal investment decision. (Copeland, Weston & Shastri)

Answer 1

Answer:

Rearrranging the investment outlay according to the rate of return, we get the following table:

Project	1+ROR	Outlay	cumulative sum	Income for C1
D	1.30	3M	3M	3*1.3 = 3.9M
B	1.20	1M	4M	3.9 + 1*1.2 = 5.1M
A	1.08	1M	5M	5.1 + 1*1.08 = 6.18M
C	1.04	2M	7M	6.18 + 2*1.04 = 8.26M

Production opportunity set represents the tradeoff between consumption today (C0 which is total investment - amount of consumption) and consumption tomorrow ( C1 which is extra returns). This tradeoff is achieved through investment.

C0 is calculated as Total outlay - outlay for the project/s (which gives us the total investment possible if that project is consumed in the current period).

So, for project D (highest ROR). C0 is (7-3 = 4M). C1 is (1.3*3 = ) 3.9M

For projects D and B (highest and next highest ROR), C0 = 7-(3+1) = 3M, C1 = (3*1.3) + (1*1.2) = (3.9 + 1.2)

= 5.1M.

For projects D, B, and A, C0 = 7- (3+1+1) = 2M; C1= (3*1.3)+(1*1.2)+(1*1.08) = (3.9+1.2+1.08)= 6.18M

Fo all projects, A,B,C and D, C0 = 0, C1 =  (3*1.3)+(1*1.2)+(1*1.08) + (2*1.04) = (3.9+1.2+1.08+2.08)= 8.26M

If all 7M is forgone in present consumption, resulting C0 and C1 plotted on the graph would look like this:

Production opportunity slopes -1.04 slope alios slope = -1.2 slope = al.3 LABL D (M. Millious)

b) If market ROR is 10%, then projects D and B would still have higher ROR, and projects A and C would have lower ROR. so it would be wise to invest in projects B and D and not to invest in projects A and C.

Then the present value of wealth of projects B and D would be

W0 = P0 + (P1/1+r) = (7- [3+1]) + 5.1/ (1+10% [market ROR ])

= 3+ (5.1/ 1.1) = 7.64M (7.64M will be the end point of market capital line on x-axis)

Total value of all four projects with ROR of D at 1.3, B at 1.2, A at 1.1 (market rate) and C at 1.1 (market rate) will be

(3*1.3) + (1*1.2)+ (1*1.1) + (2*1.1) = 3.9+1.2+1.1+2.2 = 8.4M (8.4M will be the end point of market capital line on y-axis)

Along with market capital line, the graph would look like this:

  

GT - Production - Q- Opportunity. pr set oper-1.04 6.18 Slope 108 optimal investment slope 2-102 capital market line 77.66 collious) (M. Millious)

optimal investment would be in project D and B.