Your BA II Plus
TVOM Keys
Applications: (for single cash flows)
1. The present value of a future cash flow:
$10,000 in 4 years at 10% per year
 10,000
[FV]
4
[N]
10
[I/Y]
[CPT] [PV] =
2. Number of years to a goal:
$5,000 today, $12,000 goal, 8% per year
 -5,000,
[PV]
12,000
[FV]
8
[I/Y]
[CPT] [N] =
3. Interest required to reach a goal:
$5,000 today, $12,000 goal, 10 years allowed
 - 5,000
[PV]
12,000
[FV]
10
[N]
[CPT] [I/Y] =
4. Future value of a current investment:
$3,000 today, invested for 10 years at 12 % per year
 -3,000
[PV]
10
[N]
12
[I/Y]
[CPT] [FV] =
Applications (single cash flows and compounding)
5. (From # 1 above)
The present value with interest compounded monthly:
 $10,000
[FV]
4 x 12 =
[N]
10 ÷ 12 =
[I/Y]
[CPT] [PV] =
6. (From # 4 above)
The future value with quarterly compounding:
 -3,000
[PV]
10 x 4 =
[N]
12 ÷ 4 =
[I/Y]
[CPT] [FV] =
Applications (multiple cash flows)
7. The present value of a series of future cash flows:
$ 2,000 per year for 40 years at 10%
 - 2,000
[PMT]
40
[N]
10
[I/Y]
[CPT] [PV] =
8. Number of years to a goal:
$250,000 at retirement with $4,000 annual payments at 9%
 250,000
[FV]
- 4,000
[PMT]
9
[I/Y]
[CPT] [N] =
9. Interest required to fund a child's education:
$2,000 annual payments for 17 years with $90,000 required
 - 2,000
[PMT]
17
[N]
90,000
[FV]
[CPT] [I/Y] =
10. Future value of your retirement account:
$2,000 payment at 9% for 40 years
 - 2,000
[PMT]
9
[I/Y]
40
[N]
[CPT] [FV] =
11. Monthly payment on a car loan:
$25,000 loan at 9% per year for 5 years
 25,000
[PV]
9 ÷ 12 =
[I/Y]
5 x 12 =
[N]
[CPT] [PMT] =
12. Monthly house payment:
$200,000 loan at 7% for 20 years
 200,000
[PV]
7 ÷ 12 =
[I/Y]
20 x 12 =
[N]
[CPT] [PMT] =
13. Effective interest on a time-share purchase:
$450 per month on a $15,000 loan for 15 years
 - 450
[PMT]
15,000
[PV]
15 x 12 =
[N]
[CPT] [I/Y] =
(Multiply answer by 12 to get the annual rate)
14. Number of months to pay off a construction loan:
$1,000,000 at 9½ % with 55,000 monthly payments
 1,000,000
[PV]
- 55,000
[PMT]
9.5 ÷ 12 =
[I/Y]
[CPT] [N] = 19.7089
(Multiply fraction of N by 55,000 to get final payment or .7089 x 55,000 = $38,898.50)
15. Number of months with a monthly allowance from a "mature" retirement account:
Drawing $5,000 per month from a $500,000 account earning 7% per year.
 - 5,000
[PMT]
500,000
[PV]
7 ÷ 12 =
[I/Y]
[CPT] [N] =
Now, the Amortization function!
16. First year's interest on # 12 above.
 200,000
[PV]
7 ÷ 12 =
[I/Y]
240
[N]
[CPT] [PMT] = $ 1,550.59
With the payment in the calculator, hit …..
2nd, Amort, P1 = 1, [ENTER], [] (with the analysis period starting with the 1st payment)
P2 = 12, [ENTER], [] (with the analysis period ending with the 12th payment)
BAL = 195,242.09, []
PRN = -4,757.90, []
INT = - 13,849.27.
Results reveal a $195,242 balance after one year (12 payments) on the mortgage, $4,757.90
paid in the first year in principle and $13,849.27 in interest.
17. Last year's interest on the loan in # 12:
With the results of # 16 still in your calculator, hit the "up" arrow [] 4 times;
You return to "P1 = 1". Set P1 equal to 229, P2 equal to 240.
This instructs the calculator to provide principal and interest data on the last 12 monthly
payments of a 240-month loan or the last year of a 20-year loan.
With P1 = 229, P2 = 240, [], and
BAL = -0.0163, [],
PRN = -17,920.44, [],
INT = -686.72. These results are intuitively appealing. Why? Because much less interest is
paid in the last year (686.72), than in the first year (13,849) of the mortgage.
Finally, we examine the cash flow [CF] keys toward computing such values as the
[IRR] and [NPV].
18. What is the value to the firm of a $250,000 computer system saving $55,000 per year for 7
years if the firm has a required rate of return of 8.25 %?
Using the [TVOM] keys, we know:
 55,000
[PMT]
7
[N]
8.25
[I/Y]
[CPT] [PV] = 283,918, and …..
NPV = PV(I) – PV(O) = 283,918 - 250,000 = 33,918
Using the [CF] keys?
 CFo, -250,000, [ENTER], [],
CO1, 55,000, [ENTER], [],
FO1, 7, [ENTER], [],
[NPV], I = 8.25, [ENTER], [],
[NPV], [CPT], [NPV] = 33,918
19. With 33,918 from problem # 18 still in your calculator, hit the [IRR] key, then hit [CPT].
We find [IRR] = 12.1269. (We simply used data in the CF function to calculate the IRR)
Now hit the [NPV] key.
Change I to I = 12.12 (a number very close to 12.1269!), [ENTER], [],
[NPV], [CPT], [NPV] = 54.37.
For a $ 250,000 investment, this is the discount rate that forces the NPV to “0;” this is the
IRR. (Against 250,000, 54.37 is close “enough” to 0 for our purposes.)
20. Clear your calculator by hitting the [CF] key followed by 2nd, [CLR Work].
Suppose our $250,000 computer now has irregular cash flows of $50,000 the first 4 years and
$40,000 the last 3 years and $50,000 salvage value at the end of 7 years. Our first cash flow is
still -250,000, cash flow years 1-4 are $50,000, years 5 and 6 the flows are $40,000 and we
get ($40,000 plus $50,000) $90,000 in year 7. Thusly:

CFo, - 250,000, [ENTER], [],
CO1, 50,000, [ENTER], [],
FO1, 4, [ENTER], [],
CO2, 40,000, [ENTER], [],
FO2, 2, [ENTER], [],
CO3, 90,000, [ENTER], [],
FO3, 1, [ENTER], [],
[NPV], I = 8.25, [ENTER], [],
[NPV], [CPT], [NPV] = 18,129.
21. Much more is done with the [CF] key, but a final application is presented.
Suppose we are investing $100,000 in a system generating a $20,000 cash flow for 6 years
and a $10,000 cash flow for 4 years.
What is the IRR?
 CFo, 2nd, CLR Work, -100,000, [ENTER], [],
CO1, 20,000, [ENTER], [],
FO1, 6, [ENTER], [],
CO2, 10,000, [ENTER], [],
FO2, 4, [ENTER], [],
[IRR], [CPT], [IRR] = 11.3279
22. To compute the NPV at 10 %?
With 11.3279 still in you calculator,
hit the [NPV] key, I = 10, [ENTER], [],
[NPV], [CPT], [NPV] = 4,998.
Showing a positive NPV where our discount rate is less than our IRR of 11.3279%.
"Exotic" Applications?
23. Compute the value of a bond maturing for a face value of $1,000 in 20 years, paying a 6%
coupon annually with a market required yield-to-maturity (YTM) of 7 %.
 1,000,
[FV]
20
[N]
60
[PMT]
7
[I/Y]
[CPT] [PV] = 894.05, where PV or market value<face asYTM>coupon.
24. Compute the YTM on a bond selling today for $1,030, with a 9% coupon maturing in 6 years.
 1,000
[FV]
- 1,030
[PV]
90
[PMT]
6
[N]
[CPT] [I/Y] = 8.34, where YTM<coupon as market value>face.
25. "Back door" route to mortgage (car loan) balances using the TVOM keys.
What is the balance after 10 years of a 30-year $100,000 mortgage at 7 % with monthly
payments?
 100,000
[PV]
7 ÷ 12 =
[I/Y]
30 x 12 =
[N]
[CPT] [PMT] = 665.30
120
[N]
[CPT] [FV] = 85,812.
After 120 payments (10 years) the loan's value will be $85,812.
That is the balance after 10 years.