Intro to Finance

...

= PV(0.05,25,10000) = 140,939; discounting applies to future money due to interest rate

You plan to attend a business school and you will be forced to take out $100,000 in a loan of 10%. You want to figure out your yearly payments, given that you will have 5 years to pay back the loan.

PV = 100,000; r = 10%, n = 5

=pmt(0.1,5,100000) = 26,380

2.7 Loan: The Power of Finance

All value is determined by standing at a point in time and looking forward.

Value cannot be created borrowing and lending, but by creating new idea to the society.

2.8 Compounding

Simple Interest

Compound interest

You plan to attend a business school and you will be forced to take out $100,000 in a loan of 10%. You want to figure out your yearly payments, given that you will have 5 years to pay back the loan.

What are your monthly payments, given that you will have 5 years to pay back the loan?

What is your ‘real’ annual Interest rate?

- Change in Timeline

r=10% annual; r/month = 0.1/12; 5 years -> 60 months; PV =100,000

= PMT(0.1/12,60,100000) = 2124.7

How much do you own the bank after 30 month?

= PV(PMT=2125, r=0.1/12,n=30)

Actual interest rate is higher than 10% due to compounding

Effective Annual Rates (EAR) = (1+r/k)^k -1 = (1+0.1/12)^12 -1 = 10.47%

k = number of periods within the year = 12

10% Stated vs 10.47% actual

2.9 VALUING PERPETUITIES

Perpetuities: A set of equal payments that are paid forever, with or without growth. (C---C---C---C---……)

- Bond vs Stock (Goes on forever vs Limited in maturity)

- PV = C/(r-g), if cashflow/payment = $10, Interest rate 10%, PV =$100

- g = growth rate; growth stocks

Suppose you are 30 years old. You believe that you will be able to save for the next 20 years, until you are 50. For 10 years following that, and till your retirement at age 60, you will have a spike in your expenses due to your kids’ college expenses, weddings, etc., and you will not be able to save. If you want to guarantee yourself $100,000 per year starting on your 61st birthday, how much should you save every year, for the next 20 years, starting at then end of this year. Assume that your investments are expected to yield 8% and you are likely to live till 80.

PV year 60(0.08,20,100000) = $981,814

PV year 50(0.08,10,0,981813) = $454,770

PMT(0.08,20,0,454770) = $9937.7

Contribution of ~ 10,000 for 20 times yields 100,000 x 20 due to the value of time of 8% in this case.

Suppose you are 30 years old, you believe that you will be able to save for the next 20 years, until you are 50. For 10 years following that and till your retirement at age 60, you will have a spike in your expenses due to your kids’ college expenses wedding etc. And you will not be able to save. If you want to guarantee yourself $8000 per month starting one month after your 60th birthday, how much should you save every month, for the next 20 years starting at the end of next month. Assuming that your investments are expected to yield 8% annually and you are likely to live till 80.

PMT = 8000

n = 240

r = 0.08/12

PV (at 60) = 956,434

PV (at 50) = PV (0.08/12, 120, 0, 956434) = 430896

Saving required per month = PMT = PMT (0.08/12, 240, 0, 430896) = 731.55

3.2 Decision Criteria: NPV

Context building:

- Start with an idea/project -> value creation

- A collection of ideas/projects is a firm/company

- Value creation only through good idea/projects

- How do you determine what is a good idea/project?

Properties of a good decision criterion:

- Makes sense (benefits exceed costs) or gain > pain

- Unit of measurement

- Benchmark obvious

- Easy to communicate

- Easy to compare different ideas/projects

- Easy to calculate

Net Present Value (NPV) = subtracting the investment cost (NPV vs PV)

Assume an interest rate of r=10% what is the NPV of this idea?

Year

Cash Flow

Year to Discount (n)

Present Value (PV)

0

-1000

0

-1000

1

1320

1

1320/(1+0.1)=1200

NPV

200

Intuition:Where do the “cash flows” come from? Where did the money come from?

- Cash belongs to the project, the idea. Then one will be responsible to generate the cost vs benefits.

-