ADMS 3530 Final Review Session – Solutions
Example 1: Multiple Cash Flows
Answer B
Detailed solution:
0 1 2 r = 4%
|-----------|-------------I FV2= $3032.32
$200 “Y” 2400
You can use either
Option a) FV formula and bring all cash flows to t=2 or
Option b) PV formula and bring all cash flows to t=0
Option a) Bring all cash flows to t=2 (use FV or compound)
2 1
200(1 + r)2+ Y(1 + r) + 2400 = 3032.32
200(1.04) + Y (1.04) + 2400 = 3032.32
216.32 + Y(1.04) + 2400 = 3032.32
Y(1.04) = 3032.32 – 2400 – 216.32
Y(1.04) = 416
Y = 416 / (1.04)
Y = $400
Option b) Bring all cash flows to t=0 (use PV and discount)
1 2 2
200 + Y/(1 + r) + 2400/(1 + r) = 3032.32/ (1 + r )
Y = $400.00
Example 2: Delayed Annuity
Answer A
Using your calculator:
PMT = $100, I = 9, n= 4, Fv =0, COMP PV
PV = $323.97 at t=1 !!
Bring PV 1o PV 0
PV = $323.97 / (1.09) = $297.22
0
Example 3: EAR
Answer D
Using your calculator: PMT = $1883.33, n = 12, PV = $20,000, FV=0, Comp “i”
i= 1.9322%
EAR = (1+.019322) -1 = 25.82%
Example 4: Mortgages
Answer D
3530 Final Tutorial - Solutions.F11 1 The monthly interest rate is given by:
(1 + im ) = 1 + EAR = (1 + 3125%)² = 1.076406, that is im = 0.5142%
The monthly payment for the 20-year loan
320,000 = PMT x PVIFA(0.5142%,300)
PMT = $2,095.22
Mortgage remaining at the end of 5 years 240 months remaining:
Using your calculator:
PMt = $2095.22, n=240, i=.5142, Fv=0, COMP PV
PV = 288,480.10
Example 5: Bonds
Solution
a) Current Yield = Annual Coupon Payment/ Bond Price
Step 1: Find price of bond today (7 years remaining)
Using your calculator:
PMT = 70/2 = 35.00, n = 7 x 2 = 14, FV = 1000, i = 8/2 = 4%, COMP PV
PV = -947.18
-> Current Yield = $70/$947.18 = 7.39%
Step 2: Find rate of return over holding period (3 years)
b) Rate of Return = (Coupon Interest + Price Change) / Initial Price
= [70 x 3 + (947.18 – 1000) ] / 1000
= [210 + (-52.82)] / 1000
= 15.718% (over 3 years)
Step 3: Find annual rate of return
EAR = (1 + .15718) 1/3-1 = 4.99%
Example 6A: Stocks
Answer D
DIV 0 $2.00
->Div1= 2.00 (1+g) 1
->Div4= 2.00 (1+g) = 2 x (1 + 5%) = 2.43 and
P 3 DIV /4(r – g)
= 2.43 / (11% - 5%) = $40.52
Example 6B)
Answer is $10.18 (try working it our yourself!)
Example 7
Solution C
Payback = 2 + $300/$500 = 2.6 years
CF0 = -1000; CF1 = 400; CF2 = 300; CF3 = 500; CF4 = 400; I = 10
NPV = $260.43 ≈ $260; IRR = 21.22%
3530 Final Tutorial - Solutions.F11 2 Example 7: EAC
Answer B
You need to find EAC of $8,000 today, then calculate how much more per year you can spend
on annual maintenance so you pay the equivalent of $4,000 per year total.
EAC = PV[annual PMT] = $8,000
Using your calculator:
I = 8, n=4, PV = $8,000, FV=0 , Comp PMT
PMT = $2,415.89
Thus, annual maintenance costs must be less than: $4,000 - $2,415.39 = $1,584.61 (B)
When combined with the annuitized cost of the vehicle, any annual expense over $1,584.61
would place the total annual expense of the new vehicle over $4,000.
Example 8 D

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