Time Value of Money

• Time Value of Money - one pound today is worth more than a pound promised at some time in the future because you can invest it and earn interest.
• Present Value = Discounted Cash Flow
• Simple interest investment: Investment * r * t
• When we consider future cash flows, we use expected returns
• When considering past cash flows, we calculate realised returns.
• Future Value with Multiple Cash Flows = PV * (1 + r)^t + PV * (1 + r)^t-1 … + PV * (1 + r)^1 + PV
• Annuity Formula (when the stream of cash flows is constant): PV = C / r * [1 - 1/(1+r)^n]
• Annuity Formula (when the stream of cash flows grows at a constant rate): PV = C / r * [1 - (1+g)/(1+r)^n]
• Perpetuity Formula (no growth rate): PV = C / r
• Perpetuity Formula (with growth rate): PV = C / (r - g)
• Perpetuity is used when the investment grows forever
• EAR = (1 + r / n)^n - 1