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There are two tech startups in Shenzhen, DigitalX and SpaceY. Both of them are limited liability...

There are two tech startups in Shenzhen, DigitalX and SpaceY. Both of them are limited liability companies, but they differ in their capital structure. DigitalX is 40% debtfinanced and 60% equity-financed, while SpaceY is 60% debt-financed and 40% equityfinanced. Suppose each company has RMB 10 million of assets. Both firms pay 10% interest rate on their debt. As the Shenzhen government is the main supporter of these startups in this stage, their economic outlook depends on Shenzhen government’s fiscal policy. If the government adopts a loose fiscal policy, then both firms make RMB 2 million in a year. If the government adopts a tight fiscal policy, then both make RMB 1 million in a year. The loose fiscal policy scenario happens with probability 80% and the tight fiscal policy scenario happens with probability 20%. i) Recall that a balance sheet has three components, assets, debt, and equity. Write down the values of assets, debts and equity (in millions) under “Asset”, “Debt”, and “Equity” respectively on DigitalX’s balance sheet. Write down the values of assets, debts and equity under “Asset”, “Debt”, and “Equity” respectively on SpaceY’s balance sheet. ii) If you are considering to invest in DigitalX by buying a share of the firm, what is the expected return on equity? What is the standard deviation of the yearly returns? iii) If you are considering to invest in SpaceY by buying a share of the firm, what is the expected return on equity? What is the standard deviation of the yearly returns? iv)How does the capital structure in a firm affect the expected return on equity and its riskiness?

Solutions

Expert Solution

Ans i)
Balance Sheet of Digital X
Assets Amt RMB Million Liabilities & Equity Amt RMB Million
Debt                                      4
Equity                                    6
Total Asset                                     10 Total Debt & Equity                                  10
Balance Sheet of Space Y
Assets Amt RMB Million Liabilities & Equity Amt RMB Million
Debt                                      6
Equity                                    4
Total Asset                                     10 Total Debt & Equity                                  10
Ans ii)
Assuming given earnings are Net income after interest and tax.
Expected Earning
Scenario Earning Probability ROE Probability Weighted ROE Deviation of Probability Weighted ROE And Expected earning Square of Deviation of Probability Weighted ROE And Expected earning Probability*Square of Deviation of Probability Weighted ROE And Expected earning
Loose fiscal policy 80% 33%                              0.26                            (0.03)                           0.00                              0.0009
Tight Fiscal policy 20% 17%                              0.03                            (0.26)                           0.07                              0.0139
Expected Earning                              0.30                              0.0149
So Variance =                                  0.54
Std Deviation =Sq Rt of Variance=12.19%
Details Expected Earning Loose fiscal policy Tight Fiscal policy
Equity of Digital X                                    6.0                                 6.00                              6.00
Expected Earning                                  1.80                                 2.00                              1.00
Return on Equity 30.00% 33% 17%
Std deviation of expected return =12.19%
Ans iii)
Details Expected Earning Loose fiscal policy Tight Fiscal policy
Equity of Space Y                                    4.0                                 4.00                              4.00
Expected Earning                                  1.80                                 2.00                              1.00
Return on Equity 45.00% 50% 25%
Std deviation of expected return =14.36%
Scenario Earning Probability ROE Probability Weighted ROE Deviation of Probability Weighted ROE And Expected earning Square of Deviation of Probability Weighted ROE And Expected earning Probability*Square of Deviation of Probability Weighted ROE And Expected earning
Loose fiscal policy 80% 50%                              0.40                              0.10                           0.01                              0.0083
Tight Fiscal policy 20% 25%                              0.05                            (0.25)                           0.06                              0.0123
Expected Earning                              0.45                              0.0206
So Variance =                                  0.54
Std Deviation =Sq Rt of Variance=14.36%
Ans iv)
As the weight of debt in a capital structure increased , the ROE and Risk
both increases

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