Question

Xia Corporation is a company whose sole assets are $ 100, 000 in cash and three projects that it will undertake. The projects are​ risk-free and have the following cash​ flows: 

Project Cash Flow Today Cash Flow in One Year

A -$ 21,000 $ 27,000

B -$15,000 $30,000

C -$ 56,000 $ 82,000

Xia plans to invest any unused cash today at the​ risk-free interest rate of 10.6 %. In one​ year, all cash will be paid to investors and the company will be shut down. a. What is the NPV of each​ project? Which projects should Xia undertake and how much cash should it​ retain? b. What is the total value of​ Xia's assets​ (projects and​ cash) today? c. What cash flows will the investors in Xia​ receive? Based on these cash​ flows, what is the value of Xia​ today? d. Suppose Xia pays any unused cash to investors​ today, rather than investing it. What are the cash flows to investors in this​ case? Based on these cash​ flows, what is the value of Xia​ today? e. Explain the relationship in your answers to parts ​(b​), ​(c​), and ​(d​).

Answer 1

a). Project NPVs: Since the projects are risk-free, the discount rate will be the risk-free interest rate of 10.6%

Project	CF0	CF1	PV of CF1 CF1/(1+10.6%)	NPV (CF0 + PV of CF1)
A	(21,000.00)	27,000.00	24,412.30	3,412.30
B	(15,000.00)	30,000.00	27,124.77	12,124.77
C	(56,000.00)	82,000.00	74,141.05	18,141.05

Total investment required in the three projects = 21,000 + 15,000 + 56,000 = 92,000

Since the company has 100,000 in cash, it can invest in all three projects (all three have positive NPVs). Retained cash will then be 100,000 - 92,000 = 8,000

b). Total value of Xia today = total cash + project NPVs

= 100,000 + 3,412.30 + 12,124.77 + 18,141.05 = 133,678.12

c). After 1 year, investors will receive the cash flows from the projects and the total amount of retained cash invested at 10.6% for a year

= 27,000 + 30,000 + 82,000 + (8,000*(1+10.6%)) = 139,000 + 8,848 = 147,848

Based on the cash flow of 147,848 after 1 year, the value of the company today is the present value of 147,848 which is

147,848/(1+10.6%) = 133,678.12

d). If investors receive the retained cash today and the cash flows from the projects after 1 year then the cash flows will be:

Cash flow today (CF0) = 8,000

Cash flow after 1 year (CF1) = 27,000 + 30,000 + 82,000 = 139,000

Value of the company today = 8,000 + 139,000/(1+10.6%) = 8,000 + 125,678.12 = 133,678.12

e). The answers for parts b,c and d are the same. This is so because the timing of the cash flows is irrelevant. The value of the company will always be the sum of the present value of all future cash flows. If the company pays retained cash (8,000) to its investors today then they can obtain the same amount by investing it at 10.6% for a year (8,848). Similarly, they can borrow 8,000 today against the expected future cash flow of 8,848.