Capital Budgeting & DCF

1)Payback period
period(in years) = Investment/Annual Return(Cash revenue)

2)NPV [calc periodic(ie cashflow) NOT lump sum]

A is annual payment, P is loan, i interest, r no. of years
Just inverted when calculating P

**Meaning**
An annunity/loan P @ i interest will give/require A payment at the end of r years.
ie, annunity $10 @ 5% interest 5 years
A = 10(1.05⁵(.05)/[1.05⁵-1]) = 10*.231=$2.31
Year 1) P = 10*1.05 - $2.31 = $8.19 (5% interest then give $2.31)
Year 2) P = 8.19*1.05 - $2.31 = $6.2895 (5% interest then give $2.31)
Year 3) P = 6.29*1.05 - $2.31 = $4.2945 (5% interest then give $2.31)
Year 4) P = 4.29*1.05 - $2.31 = $2.19 (5% interest then give $2.31)
Year 5) P = 2.19*1.05 - $2.31 ~ 0 (5% interest then give $2.31)

Example
Investment = 30K
Discount rate, r = 20%
Annual Return = 11K
Useful life = 10 years
Scrap Value = 1K

NPV (discount scrap)
= -30K + 1K/1.2¹⁰ + [11K * (1/1.2 + 1/1.2² + ... + 1/1.2¹⁰ )]
= -29.838K + 11K * [(1.2¹⁰-1)/1.2¹⁰/0.2] (using formula above)
= -29.838K + 11K * 4.192
~ $16274

3) Break even example
27K = net annual return × 4.192 (from above)
6441 = 10% of cash(to factory) + 3.7K
2741 = (0.1)Min. Annual Sales
Min Annual Sales = 2741/0.1 = 27410

4)IRR
a)Discount rate, r that NPV = 0
b)Iteratively test to find IRR


5)Hire purchase(eg Car)[principal instead of remaining to calc interest]
Example
$50 @ 0.06 for 10 years
Total Payment = (50 + 50 * (0.06) * 10 =$80
Annual Payment = 80/10 = $8
Compare NPV, Annual Payment = $6.79

6)Additional formula based on 2)
a) Sinking fund
Info on sinking fund
FUTURE VALUE of money

Without the (1+i)ⁿ, it is the FUTURE VALUE of the money
With (1+i)ⁿ, it is PRESENT VALUE of money (< than FUTURE)

b) Present value, given infinite Period