Corporate Finance Live Session 1 Slides.pdf

Corporate Finance

1. Present Value of a Cash Flow
What could I receive (or pay off) today?
•Suppose a cash flow ????????????
????????????is coming at time ????????????, and the appropriate discount rate (given
the risk of the cash flow) is ????????????. The present value (PV)of the cash flow
????????????????????????=????????????
????????????⋅1+????????????
−????????????
=
????????????
????????????
1+????????????
????????????
=????????????
????????????⋅
1
1+????????????
????????????
•PV is what the future cash flow is worth today, i.e., what cash flow right nowis
equivalentto receiving (or paying) that future cash flow.
•Let’s do exercises 1 and 2

2. Present Value of a Cash Inflow (Exercise 1)
What could I receive(or pay off) today?
•Suppose you will receive a payment of $100,000 six periods from now. If the
discount rate is ????????????=7%per period, what is the PV of the payment?
????????????????????????=
????????????
????????????
1+????????????
????????????
=
100000
1.07
6
=66,634.22
•PV is what I could borrow today so I’m able to exactly (not too little, not too much) pay off the loan with the future cash flow. It’s what I can get today.
•If I take out a loan of 66,634.22, then I will owe at time 6:
OweatTime6=66,634.22⋅1.07
6
=100,000
and my inflow at time 6 will be exactlyenough to pay off the loan.

3. Present Value of a Cash Outflow (Exercise 2)
What could I receive (or pay off) today?
•Suppose you will owe a payment of $50,000 three periods from now. If the discount
rate is ????????????=5%per period, what is the present value of this future outflow? Since this
is an outflow, the PV should be given as a negative.
????????????????????????=
????????????
????????????
1+????????????
????????????
=
−50000
1.05
3
=−43191.88
•The 50,000 future outflow is worth an outflow today of 43,191.88. That is how much I need to set aside today (and invest at ????????????) to have enough for the outflow in the future.
•If I set aside 43,191.88 today, investing it at the discount rate of 5%(an outflow
today), then in 3 periods, I will have exactly what I need to pay the outflow ????????????
????????????:
43191.88⋅1.05
3
=50,000

4. Present Value of a Cash Flow
Summary of Meaning
•If ????????????
????????????is a future inflow…think of ????????????????????????as the amount you could borrow today and have
just enough to pay off the loan (with interest) when the future cash inflow arrives.
•If ????????????
????????????is a future outflow…think of ????????????????????????as the investment (an outflow today) you would
need to set aside and save, so you would have exactly enough to pay off ????????????
????????????at time ????????????.

5. Future Value of a Cash Flow
What could I receive (or pay off) in the future?
•While PV is converting future cash flows into present-day values, Future Value is
doing just the opposite: taking present values and converting them into future cash
flows.
•Given a present value ????????????????????????of a cash flow, the Future Value at time ???????????? (????????????????????????
????????????)is equal to
????????????????????????
????????????=????????????????????????⋅1+????????????
????????????
•A cash flow has one ????????????????????????but many ????????????????????????s: one ????????????????????????
????????????for every future time ????????????>0.
One Cash Flow has One Present Value but Many Future Values
Let’s do Exercises 3 and 4. Be thinking about meaning, just like with PV.

6. Future Value of a Cash Inflow (Exercise 3)
What could I receive(or pay off) in the future?
•Suppose you have an inflow (e.g., you receive a gift) of $1,000 today. Assume ????????????=
10%. Answer the following:
i.What is the future value at time 3, i.e., ????????????????????????
3?
ii.What is the future value at time 4, i.e., ????????????????????????
4?
•The present value is ???????????????????????? =1000. The other two require the use of the formula for ????????????????????????
????????????
????????????????????????
3=????????????????????????⋅1+????????????
3
=1000⋅1+0.10
3
=1331.00
????????????????????????
4=????????????????????????⋅1+????????????
4
=1000⋅1+0.10
4
=1464.00
•What do these mean? They are telling you that if you choose to delay using your
inflow—leaving it investedat the interest rate—then you’ll have a largeramount later.

7. Future Value of a Cash Outflow (Exercise 4)
What could I receive (or pay off) in the future?
•Suppose you have an outflow of $1,000 today. For example, you owe someone a
payment of $1,000 right now. Assume ????????????=8%. Answer the following:
i.What is the future value at time 3, i.e., ????????????????????????
3?
ii.What is the future value at time 4, i.e., ????????????????????????
4?
•The present value is ???????????????????????? =−1000. The ????????????????????????s require the use of the formula for ????????????????????????
????????????
????????????????????????
3=????????????????????????⋅1+????????????
3
=−1000⋅1+0.08
3
=−1259.71
????????????????????????
4=????????????????????????⋅1+????????????
4
=−1000⋅1+0.08
4
=−1360.49
•What do these mean? The FVs tell you what you would owe in the future if instead of
paying off the $1,000 outflow today, you borrowed it (e.g., on a credit card) and let
interest accrue on your loan.
•Notice that the outflow you owe gets bigger and bigger…

8. Future Value of a Cash Flow
Summary of Meaning
•Assume a positive interest rate ????????????>0%.
•If ????????????????????????is an inflow…think of ????????????????????????
????????????=????????????????????????⋅1+????????????
????????????
as the amount you could have at time
????????????if you “delay gratification”, that is, if you invest at the discount rate ???????????? and wait to take
the (larger) inflow at time ???????????? . You’ll receive more later.
•If ????????????????????????is an outflow…think of ????????????????????????
????????????=????????????????????????⋅1+????????????
????????????
as the amount of outflow you would
pay at time ???????????? if you delay paying the outflow you owe today (through borrowing). The
outflow ????????????????????????
????????????will be a larger outflow, since you’ll owe interest on what you borrowed.
You’ll pay more later
.

9. Cash Flow Timelines
Model Time as Discrete
Time ???????????? 0 1 2
Time 0:
Now,
the immediate future,
the next millisecond
Cash Flow
Happens
Here
Cash Flow
Happens
Here
Cash Flow
Happens
Here
Events
Period 1 Period 2
Nothing
Happens
in Here
Nothing
Happens
in Here

10. Visualizing PV and FVs
Calculate Present Value first, then any FVs you need
•Suppose there is an expected inflow of $100 coming at time 2, and ????????????=5%.

11. Cash Flow Streams and Net Present Value (NPV)
Considering the costs and benefits of a decision
•So far, all examples have been one benefit (i.e., an inflow) or one cost (i.e., a cost).
•In most business decisions, there is some mixture of costs and benefits.
•We use net present value (NPV) to make decisions. There are a couple of ways to
think about NPV:
1.Total up the PV of the benefits and subtract the PV of the costs.
????????????????????????????????????=????????????????????????Benefits−PV(Costs)
2. At each time on the timeline, calculate the net inflow =inflows−outflows, then add
up all the PV’s of the net inflows
????????????????????????????????????=????????????????????????(All Net Cash Inflows)
Let’s do Exercises 5 and 6

12. Cash Flow Streams and Net Present Value (NPV)
NPV Approach 1: PV(Benefits) − PV(Costs)
At time 1, there is a cost of $300, but there will also be inflow of $100. At time 2, there will be an
inflow of $100 and at time 3, another inflow of $300. Assume ????????????=10%.
1. Calculate the ???????????????????????? of each inflow (benefit) and add them up:
????????????????????????Benefits=
100
1.10
+
100
1.10
2
+
300
1.10
3
=398.95
2. Calculate the ???????????????????????? of each outflow (expressed as a positive number) and add them up:
????????????????????????Costs=
300
1.10
=272.73
3. Calculate ????????????????????????????????????=????????????????????????Benefits−????????????????????????Costs=398.95−272.73=126.22
0 1 2 3 4
100
Timeline of Benefits
300100
0 1 2 3 4
Timeline of Costs
300

13. Cash Flow Streams and Net Present Value (NPV)
NPV Approach 2 (Best): Calculate the Net Inflow at Each Time
At time 1, there is a cost of $300, but there will also be inflow of $100. At time 2, there
will be an inflow of $100 and at time 3, another inflow of $300. Assume ????????????=10%.
1.Calculate the net inflows (all inflows − all outflows) at each point in time.
2. Calculate the ???????????????????????? of each net inflow and add up the ???????????????????????? s
????????????????????????????????????=−200⋅1.10
−1
+100⋅1.10
−2
+300⋅1.10
−3
=126.22
With either approach, you can calculate ???????????? ????????????
???????????? with the formula ????????????????????????
????????????=????????????????????????????????????⋅????????????+????????????
????????????
0 1 2 3 4
100
Cash Flow Timeline (Net Inflows)
300−200

14. NPV Rule
Positive NPV? Do the investment Negative NPV? Don’t do it
•If you have a decision to make, forecast the expected future cash flows (costs and benefits).
•Really Hard Part: Select a discount rate that reflects the risk of the cash flows.
Risk-free? Use the risk-free rate (often written ????????????
????????????), i.e., the return on U.S. Treasury Bills
Risky? Start with the risk-free rate and add a risk premium that reflects how risky the project is. Higher
risk -> Higher risk premium -> Higher discount rate
Key Idea: What return on their investment would rational investors expect on investments of similar
risk?
•If ????????????????????????????????????>0, we do the investment. If ????????????????????????????????????<0, we don’t do the investment.
•Why? Think about what ????????????????????????????????????>0 means:
NPV>0
PVBenefits−PVCosts>0
PVBenefits>PV(Costs)
It’s saying in math that the present value of the benefits outweigh the present value of the costs.

15. Note on Terminology
Same math, different implications about cash flows
0 1 2 3 4
100
Cash Flow Timeline
300200
????????????????????????=�
????????????=0
????????????
????????????
????????????
1+????????????
????????????
=
0
1+????????????
0
+
200
1+????????????
1
+
100
1+????????????
2
+
300
1+????????????
3
+
0
1+????????????
4
????????????????????????????????????=�
????????????=0
????????????
????????????
????????????
1+????????????
????????????
=
−100
1+????????????
0
+
100
1+????????????
1
+
200
1+????????????
2
+
−50
1+????????????
3
+
0
1+????????????
4
0 1 2 3 4
200
Cash Flow Timeline
−50100
−100
“PV” implies all inflows or all outflows, while “NPV” implies a mixture of outflows and inflows