Question Details

Future Value Analysis 
1.
FV of investment = investment x (1 + r)t
PV = future value after t periods/(1 + r)t
1. Future payments=3000
a. Year 1=1000
b. Year 2=0
c. Year 3=2000
If you are getting 3000 in future, the money you will loan them is less today.
2. Bank
a. 5%
b. 5%
c. 8%
FV=3000/(1.05) (1.05)2 (1.08)=2399.62
Need to calculate the PV of the money and then calculate bank interest rate
PV of a future payment =3000/(1 + r)t
Discount factor: present value of a $1 future payment
1/(1+r)t
Payment sked
0 1 2 3
1000 0 2000
r 5% 5% 8%
PV=1000/1.05 + 2000/1.05 1.05 1.08 = 2632.06
Put 1000 in the bank for 2 years: 1000 x 1.05 1.05 1.08
Ptu 2000 in bank for 1 year (3rd year ) 2000 x 1.08
Today; the 1000 is 1000/1.05
1000/1.05 + 0/(1.05)2 x 2000/(1.05)2 (1.08) (the third payment is discounted 3 times)
3000/1.05=2857.14 + 3000/(1.05)2=2722.32+3000/(1.05)2 (1.08)=2519.53
Payment in year one: 1000. What is present value of this? 1000/(1+.05)=952.38
Payment in year two: 0. Since we are not getting paid, still need to do the PV of this.
Our 1000 can be working for us during this period. 1000/(1.05)2=2721.09
Payment in year three: 2000. 2000/(1.05)2 (1.08)=1680.67
Bank loan money today : Loan(1.05)2 (1.08)
Make loan and repaid 1000 (1.05)(1.08) + 2000 (no interest)=
Thereason why you don’t do 1.05)2, because a the difference between getting the loan
now and getting it a year from now, is 5% interest.
Calculate loan from beginning and prove it by looking at the end!
Banking the loan and making the loan and getting paid back are the same!. You are
indifferent.
Problem 2.
YR 1 2 3
0 2000 2500 3000
R 5% 5% 5%
PV=2000/1.05 + 2500/(1.05)2 + 3000/(1.05)3
2 yrs later: got 2000(1.05) + 2500 + 3000/1.05= # #-PV/PV=10.25
Past reinvest Present Future discount
Banked cash flows: 2000 (1.05) + 2500
Sold remaining 3000/1.05
Problem 3
NPV: greater than zero, do it.
Now yr1 yr2 yr3
-10000 3000 4000 5000
R 4 5 6
3000 arrives after the 4% in year one, so it only gets 5 and 6%
-10000+3000/(1.04) + 4000/(1.04) (1.05) + 5000 (1.04) (1.05) (1.06)
-10000+ 2884.61 + 3663.00 + 4317.78
-10000+10865.39= 865.39 Do it.
Bank: 10000 (1.04)(1.05)(1.06)
Machine: 3000(1.05) (1.06) + 4000 (1.06) + 5000=
If you are going to spend 10k of corporate money, then compare it to what you can get
doing another investment.
4.
3%
1 10/1.03 + 20/1.03 2 + 30/1.03 3 Difference btw them/PV 1
2 30/1.03 + 20/1.03 2 + 10/1.03 3
12%
3 1 10/1.12 + 20/1.12 2 + 30/1.12 3 Difference btw them/PV1
4 30/1.12 + 20/1.12 2 + 10/1.12 3
Asset 1
CF Yr1 Yr2 Yr3
10 20 30
R 3 3 3
FV= 10 (1.03)3 + 20 (1.03)2 + 30 (1.03)
11.26 21.22 30.90 = 63.38
PV=FV after t periods/(1 + r)t 63.38/(1.03)3=58.04
R=12
FV 10 (1.12)3 + 20 (1.12)2 + 30 (1.12)
14.05 + 25.09 + 33.60 = 72.74
PV=FV after t periods/(1+r)t 72.74/(1.12)3=51.77
Asset 2
CF yr1 Yr2 Yr3
30 20 10
R 3 3 3
FV= 30 (1.03)3 + 20 (1.03)2 + 10 (1.03)
33.75 + 21.22 + 10.30 = 65.27
PV=FV after t periods/(1 + r)t 65.27/(1.03)3=59.77
R=12
FV 30 (1.12)3 + 20 (1.12)2 + 10 (1.12)
21.43 + 25.09 + 11.20 = 57.72
PV=FV after t periods/(1 + r)t = 57.72/(1.12)3=41.23
Problem 5
Annual CF+ coupon x face = .1 (1000)=100
100 100 1100
P= 100/1.05+ 100/1.05 2 + 1100/1.05 3+ P greater than face
Coupon/price= 100/price=coupon yield
Actual r=5%
Return 1 year=Coupon + change in price/price paid= 100+Change in price/1136=5%
Problem 6
P=80/1.1 2 ++++++1080/(1.1)80= 80(20 yr, 10% annuity) + 1000/(1.1)20=829
This is selling at discount.
80 80 80 (SELL HERE)
10% 10% 10%
80 ( 17 YR 10%) + 1000/(1.1)17
What is 3 year return? Return=coupon+change in price/price paid
Return 3yr=80(1.1)+80(1.1)+80+Change in price/Price paid
Check on work: did I earn the discount rate? Add one to discount rate and raise it to
power.
Change in price: Price you sell it for-Price you bought it for
Problem 7
Div grows then price is P=Do (1+g)/r-g
2 2 2 2 2(1+g) 2(1+g)2
10% 10% 10%
Growth formula assumes price now. In this example, price kicked in 4 years from now.
Have to bring the price back
P= 2/1.1+2/1.1 2+ 2/1.1 3=2/1.1 4+ 2(1.05)/.1-.05/(1.1)4------(1.1)4 brings price back!
Return over 2 years = 2 dividends + change in price/Price paid.


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