Discount Rate
1 Summary
People call What You Couldve Made the DISCOUNT RATE
\[\frac{\text{What you actually made}}{\text{What you couldve made}}\]
People call the fraction the PVR Present value ratio Or the Net Present Value ratio
2 Intro
2.1 Example
- Everyone knows Intuitively, starting with 1000 a return of 3% annually for 2 years means \(1000 \times \color{green}{(1+0.03)^2}\)
Lets break this down:
\[\color{green}{(1+0.03)^2} = \frac{(100\% + 3\%)^2}{100\%} = \frac{\text{What you actually made}}{\text{What you couldve made}}\]
What You Actually Made 103% your current money each year.
What You Couldve Made 100% meaning hypothetically if you did nothing with your money.
The Net Present Value(NPV) of your 1000 investment is 1060.9
2.2 Dual-Example
- But it is less intuitive what \(1000 \times \color{green}{\frac{1}{(1+0.03)^2}}\) means
Lets break this down:
\[\color{green}{\frac{1}{(1+0.03)^2}} = \frac{100\%}{(100\% + 3\%)^2} = \frac{\text{What you actually made}}{\text{What you couldve made}}\]
What You Actually Made 100% meaning you did nothing with your money.
What You Couldve Made 103% meaning hypothetically if you invested your money.
The Net Present Value(NPV) of your 1000 investment is 942.59
3 Extreme example
- You invested your money in 0% coupon rate bonds for 2 years, BUT inflation is 200% each year.
- Your net present value of 1000 investment in bonds for 2 years is only 250.
- Because with 1000 untouched you couldve made 4000 just from inflation.
- But you actually made 1000 for locking your money into a crap bond.
- Because with 1000 untouched you couldve made 4000 just from inflation.
- Your net present value of 1000 investment in bonds for 2 years is only 250.
The discount rate is 200% since inflation of 200% is what you couldve made
The NPV ratio for 2 years is \(\frac{\text{What you actually made}}{\text{What you couldve made}} = \frac{1000\text{ from crap bond}}{4000\text{ from impending inflation}} = 0.25\)
4 Discount rate and T-bill interest rate
People like to use Discount rate aka what you couldve made as the interest rate.
This assumes all rational actors without any investment knowledge would just throw their money in T-bills aka treasury bonds.
