Anna has access to a perfect capital market with interest rate r = 0.15 (i.e. 15%) per period. She also has the opportunity to purchase a private asset for price P. If she purchases the asset, she will be able to invest any amount z ≥ 0 in this private asset. If Anna invests z≥0 now, the asset will return R(z) = 80.5 √√2 next period. What is the largest amount P that Anna would be willing to pay for the private asset? [Hint: What is the net present value, NPV (z), of the private investment opportunity? What is the optimal investment z* that maximizes NPV (2).]

Essentials Of Investments
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ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
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Exercise 1: Optimal Safe Investment
Anna has access to a perfect capital market with interest rate r = 0.15 (i.e. 15%) per period.
She also has the opportunity to purchase a private asset for price P. If she purchases the asset, she will
be able to invest any amount z > 0 in this private asset. If Anna invests z > 0 now, the asset will return
R(z) = 80.5 · vz
next period.
What is the largest amount P that Anna would be willing to pay for the private asset?
[Hint: What is the net present value, N PV (z), of the private investment opportunity? What is the optimal
investment z* that maximizes NPV(z).]
Transcribed Image Text:Exercise 1: Optimal Safe Investment Anna has access to a perfect capital market with interest rate r = 0.15 (i.e. 15%) per period. She also has the opportunity to purchase a private asset for price P. If she purchases the asset, she will be able to invest any amount z > 0 in this private asset. If Anna invests z > 0 now, the asset will return R(z) = 80.5 · vz next period. What is the largest amount P that Anna would be willing to pay for the private asset? [Hint: What is the net present value, N PV (z), of the private investment opportunity? What is the optimal investment z* that maximizes NPV(z).]
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