Question

I need help to solve different kinds of calculations for my Managerial finance class. I want help with step by step solutions, to find the Net Present Value, Payback, Accounting Rate of Return(ARR), Internal Rate of Return, How Firms Estimate their Cost of capital, the cost of debt, cost of equity, using the WACC in practice, coupon rate, M&M proposition 1 and 2, stock splits,stock dividends and stock splits, type of dividends, the ex-dividend date, Hoe stock repurchases differ from dividends, and how stock is repurchased?

Answer 1

You have asked way too many things in the same question. I will help you out with:

Net Present Value, Payback, Internal Rate of Return

For the balance please post them as separate questions.

Net Present Value (NPV) Method

NPV method discounts all the future cash flows of the firm with the required rate of return (RRR) to obtain their present values. Present value of a future cash flow is that value of cash required today that will grow to the future value if invested at RRR. Hence, present value of a cash flow (CF_t) in period t (years) from now at a RRR of k is given by,

The present values of all the future cash inflows are aggregated and netted against the present values of all the future cash outflows to obtain NPV.

Projects with normal or conventional cash flows have outflows, or costs, in the first year (or years) followed by a series of inflows. Projects with non-normal or non-conventional cash flows have one or more outflows after the inflow stream has begun. In case, the project involves just one cash outflow in t = 0 and cash inflows in subsequent year (normal or conventional project) then,

This can be interpreted as: A project’s NPV is the present value of the project’s future expected cash flows minus the proposal’s initial cash outflow.

Internal Rate of Return (IRR) Method

IRR is the annualized effective compounded rate or return that can be earned on the capital invested. Mathematically, IRR is that discount rate at which NPV of a project (capital investment) is zero. It’s that discount rate which makes the sum of present value of all the future cash inflows same as that of all the future cash outflows.

In case of a conventional capital budgeting project (one initial cash outlay at t = 0 followed by cash inflows in all the subsequent years till the tenure of the project), IRR is that discount rate that makes the present value of all the expected incremental after-tax cash inflows just equal to the initial cost of the project. Mathematically, IRR is solution to k from the equation below:

Alternatively,

Payback Method

Payback period is the time period taken to recover the initial cost of an investment. Under payback method, the future net cash inflows are compared with the net initial investment (outflow) to determine the time it will take to recoup the net initial investment, without taking the time value of money into consideration. Payback period calculated under this method is compared with the target payback period or payback period of alternative projects while decision making. The generic decision criterion is shorter the payback period, better the project is. It is more widely used in industries where the lifecycle of the project is very short. It is also used when investor is more interested in capital preservation rather than earning interest.

In case of uniform cash flows

In case of uneven cash flows:

While you may try to remember these formulae, the easiest way to understand a payback period is the point in time when cumulative cash inflows on a project equal total cash outflows or when cumulative cash flows on a project is zero. If this happens in between two integral years, then you will have to linearly prorate between these two years.

Payback period is best to be used along with other capital budgeting methods as it ignores project’s profitability.

Payback period, unless otherwise specified, should be considered as being referred to a simple payback period where time value of money concept doesn’t play any role.