# Finance Hw Ps2-4 Essay

1680 Words Nov 10th, 2012 7 Pages
Problem Set #2
4.
(a) Assuming that all the bonds make only annual payments, what spot rates are imbedded in these prices? First, we need to find the Discount Factors:
Bond A: 〖DF〗_1*\$100=\$93.46
Bond B: 〖DF〗_1*\$4+〖DF〗_2*\$104=\$94.92
Bond C: 〖DF〗_1*\$8+〖DF〗_2*\$8+〖DF〗_3*\$108=\$103.64

〖DF〗_1=93.46/100=0.9346
〖DF〗_2=((94.92-(0.9346*4)))/104=0.8767
〖DF〗_3=((103.64-(0.9346*8)-(0.8767*8)))/108=0.8255
Since 〖 DF〗_t=1/〖(1+r_t)〗^t , we have r_t=(1/〖DF〗_t )^(1⁄t)-1. Then solving for r1, r2 and r3 we get: r_1=0.069976≅0.070 r_2=0.068008≅0.068 r_3=0.066009≅0.066 So the spot rates are: Bond A = 7%, Bond B = 6.8% and Bond C = 6.6%.

(b) What forward rates are embedded in these prices?
The formula for forward rates is:
So the company should invest \$ 2.6 million - \$ 1.6 million = \$1 million in real assets.
(c) How much will this investment be worth next year?
The value of the investment in real assets is denoted by the value of the transformation function. So the investment will be worth \$ 3 million in future.
(d) What is the average rate of return on the investment?
The average rate of return (ARR) is: ARR=3/1-1=2=200%
(e) What is the marginal rate of return?
The marginal rate of return (MRR) is: MRR=5/4-1=0.25=25% which is the slope of the point on the investment curve where the budget of the constraint curve is crossed.
(f) What is the present value of this investment? PV=3,000,000/1.25=2,400,000
The present value of this investment is \$ 2.4 million.
(g) What is the net present value of this investment? NPV=-1,000,000+3,000,000/1.25=1,400,000
The net present value of this investment is \$ 1.4 million.
(h) What is the total present value of the company?
The total present value of the company is represented by the sum of the investments present value and the present value of the cash being invested in the capital market.
So it is the maximum amount that would be available today.
\$ 2.4 million + \$ 1.6 million = \$ 4 million
(i) How much will the individual consume today?
Based on the owner´s preferred consumption pattern, he will consume \$ 1 million today (which is possible since he has \$ 1.6 million in

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