Arnë Kaiser110/27/18
MGT 890
Valuation and Investment Homework Set 1
1.
a.
Future
Value
A
B
Present Value
Different investors may value future and present benefits differently. For one investor (Green), investment A is on a higher indifference curve, while for another (Blue) investment B is higher rated. The investors would place their money depending on personal preference, and neither A or B could unanimously be called superior.
b.
Future
Value
A’
A
B
Present Value
In the presence of a financial market, money can be lent and borrowed at a given rate. Any cash flow becomes equivalent to a higher cash flow later on, or to a lower cash flow earlier on (assuming a positive interest rate). All investments of similar value will be on the same budget constraint line. This means that investing in project B would be economically the same as investing in a hypothetical project A’, which obviously is higher rated as project A (higher indifference curve). Thus, with a financial market, all investors will agree that project B is superior to project A.
c.
As seen above, all investments with similar value will be on the same budget constraint line. As all these lines are parallel, investors will chose the one that is the furthest away from the origin. To get a unique value, which allows us to compare these investments, we consider their intersection with the “present value” axis. The investments with the highest present value will be the more desirable, regardless of when the actual cash flows occur. This way, the present value allows investors to rank any investment, independently of timelines (future vs. present benefits…).
2.
The formulation of the question leaving a few doubts, we make following two assumptions:
-The interest rate of 12% is per period, whatever a period is (month, year…).
-The present moment would be period 0. Period 1, as listed, occurs later.
Project 1:
PV = 10/(1.12)3 = 7.12
Project 2:
PV = -30/(1.12) + 50/(1.12)4 = 4.99
Project 3:
PV = 40/(1.12) – 20/(1.12)2 + 30/(1.12)3 = 41.12
Project 4:
PV = -30/(1.12) – 40/(1.12)2 + 70/(1.12)3 + 10/(1.12)4 = -2.49
3.
a.
Per definition, this is an annual interest rate compounded daily. The real annual interest rate is calculated as follows:
r = [(1 + .06/365)365] – 1 = .0618 = 6.18%
The 6% given by the bank is not the interest rate.
b.
If we assume an annual interest rate of 1%, the present value is:
PV = 3400.22/(1.01) + 3400.22/(1.01)2 + 3400.22/(1.01)3 = 10,000
As this is the initial sum, our assumption is right. The annual interest rate is 1%, as given by the automobile company.
c.
Assuming an annual interest rate of 7%, the present value of this investment is:
PV = 5172.04/(1.07)1/2 = 5000
As this is the initial investment, our assumption is right. The annual interest rate is 7%, as given by the bank.
d.
Assuming an annual interest rate of 8%, the present value of this investment is:
PV = 40/(1.08).5 + 40/(1.08)1 + 40/(1.08)1.5 + 40/(1.08)2 + 40/(1.08)2.5 + 40/(1.08)3 + 40/(1.08)3.5 + 40/(1.08)4 + 40/(1.08)4.5 + 1040/(1.08)5 = 1006.31
As the present value would be higher than the initial investment, the real annual interest rate is higher than 8%. The interest rate named by the dealer is not an actual interest rate.