PRESENT VALUE OF

MIXED STREAMS OF CASH FLOWS

Present value of series of mixed payments = sum of the present value of each

individual payment.

Cost of new product line: P32,000 Year 1 = P10,000 Year 2 = P20,000 Year 3 = P5,000

YEAR CASH INFLOWS

PVF OF 10%

PRESENT VALUE

1 P 10,000 0.909 P 9,090

2 P 20,000 0.826 16, 520

3 P 5,000 0.751 3,755

TOTAL: P 29, 365

PRESENT VALUE OF

AN ANNUITY

Assume that the cash inflows from previous

situation form an annuity of P10,000 for 3 years:

= P10,000 ( PVOA of 10% in 3 years )= P10,000 ( 2.487 )= P24,870

PERPETUITIES

- an annuity for which the periodic payments

run infinitely.

Formula: = Receipt

Discount rate

A perpetual bond has an P80 per year interest payment and that the discount rate is 10%. The present value of this perpetuity is:

P = P80/0.10 = P800

DISCOUNTEDCASH FLOW (DCF)

ANALYSIS

- a valuation method used to estimate the attractiveness of an investment opportunity

- Uses future free cash flows projections and discounts it to arrive at a present value to evaluate the potential for investment

- value of DCF analysis > current cost of investment THE OPPORTUNITY IS GOOD.

APPLICATIONS OF FUTURE VALUES

AND PRESENT VALUES

1. Calculating deposits to accumulate a future sum ( Sinking Fund )

example : to determine the equal annual end-

of-year deposits required to accumulate P5,000 at the end of 5 years. Interest rate is 10%.

FVOA of 10% in 5 years = 6.105annual deposit = P5,000/6.105

= P819

example : P1,000,000 sinking fund for retirement of a bond in 30 years. Interest rate is 10%. The annual year-end contribution is:

FVOA of 10% in 30 years = 164.49= P1,000,000/164.49= P6,079.40

2. Amortized Loans

- a loan that is repaid in equal periodic payments.

Example: a loan of P200,000 for 5 years at an interest rate of 14%. The annual year-end payment on the loan is:

PVOA of 14% in 5 years = 3.433=P200,000/3.433=P58,258.08

example : a 40-month bank loan of P5,000 at a 12% annual interest rate. The monthly loan payment is:

PVOA of 1% in 40 months = 32.835= P5,000/32.835= P152.28

example : A business enterprise borrows P2,000 to be repaid in three equal installments for the next 3 years. Interest rate is 12%.

PVOA of 12% in 3 years = 2.402each payment = P2,000/2.402

= P832.64

-END-THANK YOU

FOR LISTENING!GOD BLESS…

-ANGELA D. TORRES